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1
Godoi, Juliano Damião Bittencourt de. "Problemas de autovalores de Steklov-Neumann e aplicações." Universidade Federal de São Carlos, 2012. https://repositorio.ufscar.br/handle/ufscar/5827.
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Previous issue date: 2012-03-26<br>Universidade Federal de Sao Carlos<br>In this work we will obtain four main results of existence of weak solution, three of them to elliptic partial di_erential systems with nonlinear boundary conditions and the other to elliptic partial di_erential equations with nonlinear boundary conditions associated with operator p-laplacian. These results will be obtained when there is a kind of interaction among the reaction nonlinearities and the Neumann spectra and an interaction among the boundary nonlinearities and the Steklov spectra, associated with the systems or equations. The tool that we will use is fundamentally based on minimax methods in critical point theory.<br>Obteremos no presente trabalho quatro principais resultados de existência de solução fraca, três deles para sistemas de equações diferenciais parciais elípticas com condições de fronteira não lineares e o outro para equações diferenciais com condições de fronteira não lineares associadas ao operador p-laplaciano. Estes resultados serão obtidos quando houver uma certa interação entre as não linearidades de reação e o espectro de Neumann, e uma interação entre as não linearidades de fronteira e o espectro de Steklov, associados aos sistemas ou equações. A técnica que utilizaremos está, fundamentalmente, baseada em métodos de minimax da teoria do ponto crítico.
2
Grando, Thiago. "Existência de soluções para uma classe de problemas com condição de Neumann." reponame:Repositório Institucional da UFABC, 2011.
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Malavazi, Mazílio Coronel 1983. "Problemas elípticos do tipo côncavo-convexo com crescimento crítico e condição de Neumann." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307128.
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Orientador: Francisco Odair Vieira de Paiva<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-21T19:28:36Z (GMT). No. of bitstreams: 1
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Previous issue date: 2013<br>Resumo: O resumo poderá ser visualizado no texto completo da tese digital<br>Abstract: The abstract is available with the full electronic document<br>Doutorado<br>Matematica<br>Doutor em Matemática
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Silva, Ilma Aparecida Marques. "Existencia e comportamento assintotico de soluções para uma classe de problemas de Dirichlet e uma classe de problemas de Neumann." [s.n.], 2003. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306979.
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Orientador: Djairo Guedes de Figueiredo<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-03T18:28:16Z (GMT). No. of bitstreams: 1
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Previous issue date: 2003<br>Doutorado<br>Doutor em Matemática
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Román, Parra Carlos Patricio. "Large conformal metrics with prescribed sign-changing Gauss curvature and a critical Neumann problem." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/116845.
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Ingeniero Civil Matemático<br>En esta memoria se estudian dos problemas semilineales elípticos clásicos en la literatura: el problema de la curvatura Gaussiana prescrita en dimensión 2, y el problema de Lin-Ni-Takagi con exponente crítico en dimensión 3. En ambos se encuentran soluciones con reviente cuando el valor de un parámetro involucrado se aproxima a cierto valor crítico.
En el primer capítulo se estudia el siguiente problema: Dada una función escalar $\kappa(x)$, suficientemente regular, definida en una variedad Riemanniana compacta $(M,g)$ de dimensión 2, se desea saber si $\kappa$ puede corresponder a la curvatura Gaussiana de $M$ para una métrica $g_1$, que es adicionalmente conforme a la métrica inicial $g$, es decir, $g_1=e^ug$ para alguna función escalar $u$ en $M$. Sea $f$ una función regular en $M$ tal que
\equ{f\geq 0,\quad f\not\equiv 0, \quad \min_M f=0.}
Sean $p_1,\ldots,p_n$ una colección de puntos cualesquiera en los que $f(p_i)=0$ y $D^2f(p_i)$ es no singular. Se demuestra que para todo $\la>0$ suficientemente pequeño, existe una familia de metricas conformes de tipo burbuja $g_\la=e^{u_\la}g$ tal que su curvatura Gaussiana está dada por la función que cambia de signo $K_{g_\la}=-f+\la^2$. Más aún, la familia $u_\la$ satisface
\equ{u_\la(p_j)=-4\log \la -2 \log \left(\frac{1}{\sqrt2}\log \frac{1}{\la}\right)+O(1),
\quad
\la^2e^{u_\la}\rightharpoonup 8\pi\sum_{i=1}^n\delta_{p_i},}
donde $\delta_p$ corresponde a la masa de Dirac en el punto $p$.
En el segundo capítulo se considera el problema
\equ{-\Delta u+\la u-u^5=0,\quad u>0 \quad \mbox{in }\Omega,\quad \ddn{u}=0\quad \mbox{on }\partial\Omega,}
donde $\Omega\subset \R^3$ es un dominio acotado con frontera regular $\partial\Omega$, $\la>0$ and $\nu$ denota la normal unitaria exterior a $\partial\Omega$. Se demuestra que cuando
$\la$ se apoxima por arriba a cierto valor explícitamente caracterizado en términos de funciones de Green, una familia de soluciones con reviente en un cierto punto interior del dominio existe.
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Almeida, Samuel Oliveira de. "Soluções para problemas elípticos envolvendo o expoente crítico de Sobolev." Universidade Federal de Juiz de Fora, 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/1468.
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Previous issue date: 2013-04-05<br>CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>Neste trabalho estudamos a existência de soluções para problemas elípticos
envolvendo o expoente crítico de Sobolev.
Primeiramente, investigamos a existência de soluções para um problema
superlinear do tipo Ambrosetti-Prodi com ressonância em 1, onde 1 é o primeiro
autovalor de (−Δ,1
0 (Ω)).
Além disso, estudamos resultados de multiplicidade para uma classe de equações
elípticas críticas relacionadas com o problema de Brézis-Nirenberg, com condição
de contorno de Neumann sobre a bola.<br>In this work we study the existence of solutions for elliptic problems involving
critical Sobolev exponent.
Firstly we investigate the existence of solutions for an Ambrosetti-Prodi
type superlinear problem with resonance at 1 , where 1 is the first eigenvalue of
(−Δ,1
0 (Ω)).
Besides, we study multiplicity results for a class of critical elliptic equations
related to the Brézis-Nirenberg problem with Neumann boundary condition on a
ball.
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Silva, CÃcero Fagner Alves da. "ExistÃncia e unicidade para os problemas de Dirichlet e Neumann sobre um domÃnio com fronteira suave." Universidade Federal do CearÃ, 2010. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5286.
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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>Seja Ω um domÃnio fixado em Rn com fronteira S de classe C2 e denote Ω′ = Rn Ω. Ambos Ω e Ω′ nÃo necessariamente conexos. Nessas condiÃÃes, pretendemos resolver os problemas de Dirichlet e Neumann.
No intuito da resoluÃÃo dos problemas citados, faremos um estudo daTeoria de Fredholm (operadores compactos), bem como da transformada de Kelvin, harmonicidade no infinito e dos potenciais de camada.<br>Let Ω be a fixed domain in Rn with boundary S of class C2 and denote Ω′ = Rn Ω. Both Ω and Ω′ not necessarily connected. Under these conditions, we intend to solve the problems of Dirichlet and Neumann.
In order to overcome the mentioned the problems, we will study the Fredholm theory (compact operators), the Kelvin transformed, harmonicity in the infinite and potential of the layer.
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Oliveira, Elisânia Santana de. "Multiplicidade de soluções positivas para algumas classes de problemas elípticos em R2 com condição de Neumann." Universidade Federal da Paraíba, 2012. http://tede.biblioteca.ufpb.br:8080/handle/tede/7366.
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Previous issue date: 2012-03-05<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>In this work, we prove the existence and multiplicity of positive weak solutions for some
classes of elliptic problems in plane involving exponential growth of the Trudinger-Moser type
with Neumann boundary condition. To do this, we use the method of sub and supersolution
in combination with variational methods and the maximum principle.<br>Nesta dissertação, provamos a existência e multiplicidade de soluções fracas positivas
para algumas classes de problemas elípticos no plano envolvendo crescimento exponencial do
tipo Trudinger-Moser com condição de Neumann na fronteira. Para isso, usaremos o método
de sub e supersolução em combinação com métodos variacionais e o princípio do máximo.
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Silva, Cícero Fagner Alves da. "Existência e unicidade para os problemas de Dirichlet e Neumann sobre um domínio com fronteira suave." reponame:Repositório Institucional da UFC, 2010. http://www.repositorio.ufc.br/handle/riufc/890.
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SILVA, Cícero Fagner Alves da; MUNIZ NETO, Antonio Caminha. Existência e unicidade para os problemas de Dirichlet e Neumann sobre um domínio com fronteira suave. 2010. 92f. Dissertação(mestrado)- Universidade Federal do Ceará, Pós-Graduação em Matemática, Fortaleza-CE, 2010.<br>Submitted by Rocilda Sales (rocilda@ufc.br) on 2011-10-11T12:54:48Z
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Previous issue date: 2010<br>Let Ω be a fixed domain in Rn with boundary S of class C2 and denote Ω′ = Rn Ω. Both Ω and Ω′ not necessarily connected. Under these conditions, we intend to solve the problems of Dirichlet and Neumann. In order to overcome the mentioned the problems, we will study the Fredholm theory (compact operators), the Kelvin transformed, harmonicity in the infinite and potential of the layer.<br>Seja Ω um domínio fixado em Rn com fronteira S de classe C2 e denote Ω′ = Rn Ω. Ambos Ω e Ω′ não necessariamente conexos. Nessas condições, pretendemos resolver os problemas de Dirichlet e Neumann. No intuito da resolução dos problemas citados, faremos um estudo daTeoria de Fredholm (operadores compactos), bem como da transformada de Kelvin, harmonicidade no infinito e dos potenciais de camada.
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Kist, Milton. "Novas metodologias de simulação do tipo Monte-Carlo via séries de Neumann aplicadas a problemas de flexão de placas." Universidade Tecnológica Federal do Paraná, 2016. http://repositorio.utfpr.edu.br/jspui/handle/1/1928.
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A engenharia é um campo muito rico e vasto em problemas. Mesmo considerando-se apenas o ramo da engenharia estrutural, a quantidade e a variabilidade de problemas continuam sendo muito grande. O aumento da capacidade computacional proporcionou, nos últimos anos, o desenvolvimento de métodos mais complexos e robustos (métodos estocásticos) para resolução de problemas na área de estruturas passando a considerar incerteza. A incerteza pode ser devido à aleatoriedade das propriedades materiais, condições de apoio e carregamento. Muitos dos métodos estocásticos são baseados na simulação de Monte-Carlo, no entanto o método de Monte-Carlo direto possui custo computacional elevado. Visando o desenvolvimento de novas metodologias para resolução de problemas da área de estruturas, neste trabalho de tese apresentam-se três novas metodologias aplicadas a problemas estocásticos de flexão de placas, caracterizando assim a contribuição científica da tese. Estas metodologias, denominadas de Monte Carlo-Neumann, com ajuste no limitante; Monte Carlo-Neumann, mista 1 e Monte Carlo-Neumann, mista 2, utilizam a série de Neumann associada ao método de Monte-Carlo. Para verificar a eficiência quanto a precisão e ao tempo computacional, as metodologias foram aplicadas em problemas estocásticos de flexão de Placas de Kirchhoff em bases de Winkler e de Pasternak, considerando-se aleatoriedade sobre a rigidez da placa e sobre os coeficientes de rigidez da base de apoio.<br>Engineering is a very rich and wide field in problems. Even considering just structural engineering branch, the amount and variability of problems remains very large. The increase of computational capacity provided development of complex and robust methods to solve structural problems consi- dering uncertainty. Uncertainty may be due to material property randomness, support conditions and load. Many of stochastic methods are based on Monte-Carlo simulation, however Monte-Carlo direct method has high computation cost. Aiming the development of new methodologies for solving problems of the structures area, this thesis presents three new methodologies applied to plates stochastic bending problems, characterizing the scientific contribution of the thesis. These methodologies, named Monte Carlo-Neumann λ and Monte Carlo-Neumann, with quotas establishment, Monte Carlo-Neumann, with adjustment in limiting, Monte Carlo-Neumann, mixed 1 and Monte Carlo-Neumann, mixed 2, both based on Neumann series, were applied to stochastic problems of flexion of Kirchhoff plates on Winkler and Pasternak bases, considering uncertainty about plate stiffness and stiffness coefficient of the support base.
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Nascimento, Moisés Aparecido do. "Resultados do tipo Ambrosetti-Prodi para problemas quasilineares." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/7640.
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Previous issue date: 2015-12-04<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>We present results of Ambrosseti-Prodi type to quasilinear problems involving the p-Laplace operator. We consider the scalar case and a a problem with systems of equations. In the scalar case, we work with the conditions of Neumann and Dirichlet. In the problem involving system, we consider the condition og Dirichlet. In order to get the results we use the theory of Leray-Schauder degree and a priori estimates.<br>Neste trabalho apresentamos resultados do tipo Ambrosseti-Prodi para problemas quasilineares envolvendo o aperador
p-Laplaciano. Considerando o caso escalar eu um problema com sistemas de equações. Para os casos escalares, trabalhamos com a condições de Neumann e Dirichlet, já para o problema envolvendo sistema, consideramos a condição Dirichlet. Para obter mais resultados usamos a teoria do grau de Leray-Schauder e estimativas a priori.
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Alves, Michele de Oliveira. "Um problema de extensão relacionado a raiz quadrada do Laplaciano com condição de fronteira de Neumann." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-19012011-231320/.
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Neste trabalho definimos o operador não local, raiz quadrada do Laplaciano com condição de fronteira de Neumann, através do método de extensão harmônica. O estudo foi feito com o auxílio das séries de Fourier em domínios limitados, como sendo o intervalo, o quadrado e a bola. Posteriormente, aplicamos nosso estudo, à problemas elípticos não lineares envolvendo o operador não local raiz quadrada do Laplaciano com condição de fronteira de Neumann.<br>In this work we define the non-local operator, square root of the Laplacian with Neumann boundary condition, using the method of harmonic extension. The study was done with the aid of Fourier series in bounded domains, as the interval, the square and the ball. Subsequently, we apply our study, the nonlinear elliptic problems involving non-local operator square root of the Laplacian with Neumann boundary condition.
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Limeira, Renata de Farias. "COEFICIENTE DE FUJITA PARA PROBLEMAS PARAB OLICOS N~AO LINEARES EM DOM INIOS EXTERIORES COM A CONDIC ~AO DE NEUMANN NA FRONTEIRA." Universidade Federal de Pernambuco, 2012. https://repositorio.ufpe.br/handle/123456789/11297.
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Previous issue date: 201<br>CNPq<br>Obtemos uma estimativa para a fun c~ao de Green associada ao problema de valores iniciais
e de fronteira associado a equa c~ao do calor em dom nios com fronteira Lipschitz compacta
e condi c~ao de Neumann homog^enea na fronteira. Esta estimativa viabiliza o estudo de
dois problemas parab olicos de valor inicial em dom nios exteriores com a condi c~ao de
Neumann homog^enea na fronteira. O primeiro deles consiste de um sistema acoplado e o
segundo trata-se da equa c~ao do calor n~ao linear com n~ao linearidade n~ao local no tempo.
Estabelecemos a exist^encia de solu c~oes locais, globais e de solu c~oes n~ao globais para estes
problemas, bem como determinamos o expoente cr tico de Fujita para ambos.
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LIMA, Natan de Assis. "Análise funcional não-linear aplicada ao estudo de problemas elípticos não-locais." Universidade Federal de Campina Grande, 2010. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1225.
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Previous issue date: 2010-03<br>CNPq<br>Neste trabalho usaremos algumas técnicas da Análise Funcional Não-Linear para estudar a existência de solução para os chamados Problemas Elípticos Não-Locais, entre os quais destacamos aqueles que incluem o operador de Kirchhoff [...].
* Para visualizar o resumo recomendamos do download do arquivo uma vez que o mesmo utiliza formulas ou equações matemáticas que não puderam ser transcritas neste espaço.<br>In this work we will use same techniques of Nonlinear Analysis Functional to study the existence of solutions for the some Nonlocal Elliptic Problems, among then those which include Kirchhoff operator [...].
* To preview the summary we recommend downloading the file since it uses mathematical formulas or equations that could not be transcribed in this space.
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Herbig, Anne-Katrin. "A sufficient condition for subellipticity of the d-bar-Neumann problem." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1090531326.
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Thesis (Ph. D.)--Ohio State University, 2004.<br>Title from first page of PDF file. Document formatted into pages; contains vi, 55 p. : ill. Advisor: McNeal, J.D., Dept. of Mathematics. Includes bibliographical references (p. 54-55).
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QUESNE, CAROLE. "Probleme d'ecran avec donnees de neumann singulieres." Nantes, 1996. http://www.theses.fr/1995NANT2091.
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S'etant une surface a bord, on s'interesse aux solutions d'une equation de poisson-helmholtz dans le complementaire de s, et verifiant des conditions de neumann sur chaque face de l'ecran s et une condition de radiation a l'infini. On etudie le cas ou le second membre f de l'equation de poisson-helmholtz est dans un espace a poids a l'infini et ou les donnees de neumann peuvent etre singulieres (masse de dirac par exemple). On donne un resultat d'existence et d'unicite pour les solutions u qui sont d'energie finie pres du bord de l'ecran. L'unicite est obtenue de facon classique par la condition de rellich. L'existence est montree par une methode de perturbation du probleme libre dans le cas des conditions de neumann homogenes, puis par relevement dans le cas non homogene. Un resultat de regularite de u est etabli, dans le cas d'une surface plane polygonale a angle droit ou complementaire d'un angle droit, en utilisant une formule de representation de u basee sur les techniques de wiener-hopf. On donne ensuite une formule de representation integrale generale de la solution u a l'aide de differents potentiels ; ce qui permet de ramener la resolution du probleme exterieur a la resolution d'une equation integrale hypersinguliere sur s. L'approximation numerique de u est faite par l'intermediaire de sa representation integrale, l'approximation de la solution de l'equation integrale etant faite par une methode d'elements finis d'ordre 1, nuls sur le bord de s, et avec un maillage uniforme. Des resultats numeriques sont donnes dans le cas d'un ecran plan carre et de donnees de neumann nulle sur une face de l'ecran et egale a une masse de dirac sur l'autre. Les tests numeriques ont permis de confirmer les estimations d'erreurs theorique
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Neves, Sérgio Leandro Nascimento 1984. "Sobre o número de soluções de um problema de Neumann com perturbação singular." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305907.
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Orientadores: Marcelo da Silva Montenegro, Massimo Grossi<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-20T13:53:15Z (GMT). No. of bitstreams: 1
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Previous issue date: 2012<br>Resumo: Neste trabalho, consideramos uma classe de problemas de Neumann com perturbação singular e fazemos um estudo do número de soluções do tipo "single peak" que se concentram em um mesmo ponto. Estudamos casos de concentração no interior e na fronteira do domínio. Obtemos um resultado de multiplicidade exata que relaciona o número de tais soluções com o número de zeros estáveis de um campo vetorial associado<br>Abstract: In this work, we consider a class of Neumann problems with singular perturbation and we study the number of single peak solutions which concentrate at the same point. We study concentration in the interior and at the boundary of the domain. We obtain an exact multiplicity result which relates the number of such solutions with the number of stable zeros of an associated vector field.<br>Doutorado<br>Matematica<br>Doutor em Matemática
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Alsaedy, Ammar, and Nikolai Tarkhanov. "Spectral projection for the dbar-Neumann problem." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5861/.
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Zanger, Daniel Zvi. "Regularity and boundary variations for the Neumann problem." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43460.
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Kulkarni, Mandar S. "Multi-coefficient Dirichlet Neumann type elliptic inverse problems with application to reflection seismology." Birmingham, Ala. : University of Alabama at Birmingham, 2009. https://www.mhsl.uab.edu/dt/2010r/kulkarni.pdf.
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Thesis (Ph. D.)--University of Alabama at Birmingham, 2009.<br>Title from PDF t.p. (viewed July 21, 2010). Additional advisors: Thomas Jannett, Tsun-Zee Mai, S. S. Ravindran, Günter Stolz, Gilbert Weinstein. Includes bibliographical references (p. 59-64).
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Yang, Xue. "Neumann problems for second order elliptic operators with singular coefficients." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/neumann-problems-for-second-order-elliptic-operators-with-singular-coefficients(2e65b780-df58-4429-89df-6d87777843c8).html.
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In this thesis, we prove the existence and uniqueness of the solution to a Neumann boundary problem for an elliptic differential operator with singular coefficients, and reveal the relationship between the solution to the partial differential equation (PDE in abbreviation) and the solution to a kind of backward stochastic differential equations (BSDE in abbreviation).This study is motivated by the research on the Dirichlet problem for an elliptic operator (\cite{Z}). But it turns out that different methods are needed to deal with the reflecting diffusion on a bounded domain. For example, the integral with respect to the boundary local time, which is a nondecreasing process associated with the reflecting diffusion, needs to be estimated. This leads us to a detailed study of the reflecting diffusion. As a result, two-sided estimates on the heat kernels are established. We introduce a new type of backward differential equations with infinity horizon and prove the existence and uniqueness of both L2 and L1 solutions of the BSDEs. In this thesis, we use the BSDE to solve the semilinear Neumann boundary problem. However, this research on the BSDEs has its independent interest. Under certain conditions on both the "singular" coefficient of the elliptic operator and the "semilinear coefficient" in the deterministic differential equation, we find an explicit probabilistic solution to the Neumann problem, which supplies a L2 solution of a BSDE with infinite horizon. We also show that, less restrictive conditions on the coefficients are needed if the solution to the Neumann boundary problem only provides a L1 solution to the BSDE.
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Sahutoglu, Sonmez. "Compactness of the dbar-Neumann problem and Stein neighborhood bases." Texas A&M University, 2003. http://hdl.handle.net/1969.1/3879.
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This dissertation consists of two parts. In the first part we show that for 1 k 1, a complex manifold M of dimension at least k in the boundary of a smooth
bounded pseudoconvex domain
in Cn is an obstruction to compactness of the @-
Neumann operator on (p, q)-forms for 0 p k n, provided that at some point
of M, the Levi form of b
has the maximal possible rank n − 1 − dim(M) (i.e. the
boundary is strictly pseudoconvex in the directions transverse to M). In particular,
an analytic disc is an obstruction to compactness of the @-Neumann operator on
(p, 1)-forms, provided that at some point of the disc, the Levi form has only one
vanishing eigenvalue (i.e. the eigenvalue zero has multiplicity one). We also show
that a boundary point where the Levi form has only one vanishing eigenvalue can
be picked up by the plurisubharmonic hull of a set only via an analytic disc in the
boundary.
In the second part we obtain a weaker and quantified version of McNealÂs Property
( eP) which still implies the existence of a Stein neighborhood basis. Then we give
some applications on domains in C2 with a defining function that is plurisubharmonic
on the boundary.
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Alcántara, Bode Julio, and J. Yngvason. "Algebraic quantum field theory and noncommutative moment problems I." Pontificia Universidad Católica del Perú, 2013. http://repositorio.pucp.edu.pe/index/handle/123456789/96072.
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Alsaedy, Ammar, and Nikolai Tarkhanov. "Normally solvable nonlinear boundary value problems." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6507/.
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We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators.
Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.
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Guo, Sheng. "On Neumann Problems for Fully Nonlinear Elliptic and Parabolic Equations on Manifolds." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1571696906482925.
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Karimianpour, Camelia. "The Stone-von Neumann Construction in Branching Rules and Minimal Degree Problems." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34240.
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In Part I, we investigate the principal series representations of the n-fold covering groups of the special linear group over a p-adic field. Such representations are constructed via the Stone-von Neumann theorem. We have three interrelated results. We first compute the K-types of these representations. We then give a complete set of reducibility points for the unramified principal series representations. Among these are the unitary unramified principal series representations, for which we further investigate the distribution of the K-types among its irreducible components.
In Part II, we demonstrate another application of the Stone-von Neumann theorem. Namely, we present a lower bound for the minimal degree of a faithful representation of an adjoint Chevalley group over a quotient ring of a non-Archimedean local field.
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Raynor, Sarah Groff 1977. "Regularity of Neumann solutions to an elliptic free boundary problem." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29353.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.<br>Includes bibliographical references (p. 57-58).<br>We examine the regularity properties of solutions to an elliptic free boundary problem, near a Neumann fixed boundary. Consider a nonnegative function u which minimizes the functional ... on a bounded, convex domain ... This function u is harmonic in its positive phase and satisfies ... along the free boundary ... , in a weak sense. We prove various basic properties of such a minimizer near the portion of the boundary ... on which ... weakly. These results include up-to-the boundary gradient estimates on harmonic functions with Neumann boundary conditions on convex domains. The main result is that the minimizer u is Lipschitz continuous. The proof in dimension 2 is by means of conformal mapping as well as a simplified monotonicity formula. In higher dimensions, the proof is via a maximum principle estimate for ...<br>by Sarah Groff Raynor.<br>Ph.D.
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Orey, Maria de Serpa Salema Reis de. "Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems." Doctoral thesis, Faculdade de Ciências e Tecnologia, 2011. http://hdl.handle.net/10362/8677.
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Dissertação para obtenção do Grau de Doutor em
Matemática<br>The purpose of this thesis is the factorization of elliptic boundary value problems defined in cylindrical domains, in a system of decoupled first order initial value problems. We begin with the Poisson equation with mixed boundary conditions, and use the method of invariant embedding: we embed our initial problem in a family of similar problems, defined in sub-domains of the initial domain, with a moving boundary, and an additional condition in the moving boundary. This factorization is inspired by the technique of invariant temporal embedding used in Control Theory when computing the optimal feedback, for,
in fact, as we show, our initial problem may be defined as an optimal control problem. The
factorization thus obtained may be regarded as a generalized block Gauss LU factorization.
From this procedure emerges an operator that can be either the Dirichlet-to-Neumann or
the Neumann-to-Dirichlet operator, depending on which boundary data is given on the
moving boundary. In any case this operator verifies a Riccati equation that is studied
directly by using an Yosida regularization. Then we extend the former results to more
general strongly elliptic operators. We also obtain a QR type factorization of the initial
problem, where Q is an orthogonal operator and R is an upper triangular operator. This
is related to a least mean squares formulation of the boundary value problem.
In addition, we obtain the factorization of overdetermined boundary value problems, when
we consider an additional Neumann boundary condition: if this data is not compatible
with the initial data, then the problem has no solution. In order to solve it, we introduce a perturbation in the original problem and minimize the norm of this perturbation, under the hypothesis of existence of solution. We deduce the normal equations for the overdetermined problem and, as before, we apply the method of invariant embedding to factorize the
normal equations in a system of decoupled first order initial value problems.
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Zaveri, Sona. "The second eigenfunction of the Neumann Laplacian on thin regions /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/5748.
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Strauss, Albrecht. "Integralformeln und a priori-Abschätzungen für das [delta bar]-Neumann-Problem." Bonn : [s.n.], 1988. http://catalog.hathitrust.org/api/volumes/oclc/18440543.html.
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Wanderley, Gabriela Albuquerque. "Capillary Problem and Mean Curvature Flow of Killing Graphs." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7418.
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Previous issue date: 2013-05-13<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>We study two types of Neumann problem related to Capillary problem and to the evolution of graphs under mean curvature flow in Riemannian manifolds endowed with a Killing vector field. In particular, we prove the existence of Killing graphs
with prescribed mean curvature and prescribed boundary conditions.<br>Estudamos dois tipos de problemas relacionados com a Neumann problema capilar e à evolução dos gráficos sob fluxo de curvatura média em variedades Riemannianas dotados com um campo de vetores Killing. Em particular, provamos a existência de Matar gráficos prescrito com curvatura média e condições de contorno prescritas.
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Kim, Mijoung. "The d-bar-Neumann operator and the Kobayashi metric." Texas A&M University, 2003. http://hdl.handle.net/1969/94.
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Boller, Stefan. "Spectral Theory of Modular Operators for von Neumann Algebras and Related Inverse Problems." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37397.
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In dieser Arbeit werden die Modularobjekte zu zyklischen und separierenden Vektoren für von-Neumann-Algebren untersucht. Besondere Beachtung erfahren dabei die Modularoperatoren und deren Spektraleigenschaften. Diese Eigenschaften werden genutzt, um Klassifikationen für Lösungen einiger inverser Probleme der Modulartheorie anzugeben. Im ersten Teil der Arbeit wird zunächst der Zusammenhang zwischen dem zyklischen und separierenden Vektor und seinen Modularobjekten mit Hilfe (verallgemeinerter) Spurvektoren für halbendliche und Typ $III_{\lambda}$ Algebren ($0<\lambda<1$) näher untersucht. Diese Untersuchungen erlauben es, das Spektrum der Modularoperatoren für Typ $I$ Algebren anzugeben. Dazu werden die Begriffe {\em zentraler Eigenwert} und zentrale Vielfachheit eingeführt. Weiterhin ergibt sich, dass die Modularoperatoren durch ihre Spektraleigenschaften eindeutig charakterisiert sind. Modularoperatoren für Typ $I_{n}$ Algebren sind genau die $n$-zerlegbaren Operatoren, die multiplikatives, zentrales Spektrum vom Typ $I_{n}$ besitzen. ähnliche Ergebnisse werden auch für Typ $II$ und $III_{\lambda}$ Algebren gewonnen unter der Vorausetzung, dass die zugehörigen Vektoren diagonalisierbar sind. Im zweiten Teil der Arbeit werden diese Ergebnisse exemplarisch auf ein inverses Problem der Modulartheorie angewendet. Dabei stellt sich heraus, dass die Begriffe zentraler Eigenwert und zentrale Vielfachheit Invarianten des inversen Problems sind und eine vollständige Klassifizierung seiner Lösungen unter obigen Voraussetzungen erlauben. Außerdem wird eine Klasse von Modularoperatoren untersucht, für die das inversese Problem nur ein oder zwei Lösungsklassen besitzt<br>In this work modular objects of cyclic and separating vectors for von~Neumann~algebras are considered. In particular, the modular operators and their spectral properties are investigated. These properties are used to classify the solutions of some inverse problems in modular theory. In the first part of the work the correspondence between cyclic and separating vectors and their modular objects are considered for semifinite and type $III_{\lambda}$ algebras ($0<\lambda<1$) in more detail, where (generalized) trace vectors are used. These considerations allow to compute the spectrum of modular operators for type $I$ algebras. To this end, the notions of central eigenvalue and central multiplicity are introduced. Furthermore, it is stated that modular operators are uniquely determined by their spectral properties. Modular operators for type $I_{n}$ algebras are exactly the $n$-decomposable operators, which possess {\em multiplicative central spectrum of type $I_{n}$}. Similar results are derived for type $II$ and $III_{\lambda}$ algebras under the assumption that the corresponding vectors are diagonalizable. In the second part of this work these results are applied to an inverse problem of modular theory. It comes out, that the central eigenvalues and central multiplicities are invariants of this inverse problem and that they give a complete classification of its solutions. Moreover, a class of modular operators is investigated, whose inverse problem possesses only one or two classes of solutions
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Schreffler, Morgan F. "Approximation of Solutions to the Mixed Dirichlet-Neumann Boundary Value Problem on Lipschitz Domains." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/47.
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We show that solutions to the mixed problem on a Lipschitz domain Ω can be approximated in the Sobolev space H1(Ω) by solutions to a family of related mixed Dirichlet-Robin boundary value problems which converge in H1(Ω), and we give a rate of convergence. Further, we propose a method of solving the related problem using layer potentials.
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Hladky, Robert K. "Boundary regularity of the Neumann problem for the Kohn Laplacian on the Heisenberg group /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/5811.
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Hänel, André [Verfasser]. "Singular Problems in Quantum and Elastic Waveguides via Dirichlet-to-Neumann Analysis / André Hänel." Aachen : Shaker, 2015. http://d-nb.info/1080762264/34.
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Ackermann, Nils. "Lokalisierung der niederenergetischen Lösungen eines singulär gestörten elliptischen Neumann-Problems mittels der Geometrie des Gebietsrandes." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=958029016.
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Baydoun, Ibrahim. "Transport laplacien, problème inverse et opérateurs de Dirichlet-Neumann." Thesis, Aix-Marseille 2, 2011. http://www.theses.fr/2011AIX22094.
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Le travail de ma thèse est basé sur ces 4 points :i) Transport laplacien d'une cellule absorbante :Soit un certain espèce (cellule) de concentration C(x), qui diffuse dans un milieu homogène et isotrope à partir d'une lointaine source localisée sur la frontière fermée $partial Omega_{0}$ vers une interface compact semi-perméable $partial Omega$ (membrane de la "cellule") à laquelle elle disparaisse àun taux d'absorption donné : W>=0. La concentration C (transport laplacien avec un coefficient de diffusion D) satisfaite le problème (P1) (voir la thèse). On s'intéresse à résoudre le problème (P1) en dimension dim = 2; 3 et à calculer les courants local et total à travers les frontières des $partial Omega$ et $partial Omega_{0}$ qui seront utiles pour résoudre le problèmeinverse de localisation. Pour faciliter les calculs et les rendre explicites, on prend $partial Omega$ et $partial Omega_{0}$ avec des formes géométriquement régulières, précisément des boules, en distinguant les deux cas : $Omega$ et $Omega_{0}$ sont concentriques ou non-concentriques. Pour le cas non-concentriques , on utilise la technique de transformation conforme et le développement orthogonal en série de Fourier pour résoudre le problème (P1) en cas bidimensionnel. Tandis que en cas tridimensionnel, on résout le problème (P1) en utilisant le développement orthogonal suivant les fonctions sphériques harmoniques.ii) Problème inverse de localisationOn s'intéresse dans cette partie à résoudre le problème inverse de localisation associé au problème (P1) où les domaines $Omega$ et $Omega_{0}$ sont considérés avec des formes géométriques régulières (précisément des boules) . Ce problème consiste à trouver les conditions de Dirichlet-Neumann sur $partial Omega_{0}$ (courant local, courant total) suffisantes pour déterminer la position de la cellule $partial$ (par rapport à $Omega_{0}$), dont ces conditions sont disponibles par une suite des mesures expérimentales.iii) Problème invesre géomètrique :Dans cette partie on traite un autre type de problème inverse qui consiste à trouver la forme géométrique de la cellule en sachant les conditions de Dirichlet-Neumann au bord extérieur(partial Omega_{0}) qui sont mésurables par une suite d'expérience. Ce type du problème, on l'appelle le problème inverse géométrique. On résout ce problème en utilisant des techniques concernant les fonctions harmoniques et les transformations conformes.iv) Opérateur de Dirichlet-NeumannOn étudie l'opérateur de Dirichlet-Neumann relatif au problème (P1) dans les dimension deux et trois en distinguant les deux cas concentriques et non-concentriques. Ensuite, on montre que cet opérateur de Dirichlet-Neumann engendre certain semi-groupe qu'on l'appelle semi-groupe de Lax. Enfin, on construit ce semi-groupe de Lax associé à cet opérateur en cas tridimensionnel concentriques afin de vérifier que ce semi-groupe admet les mêmes propriétés que celui dans le cas général<br>The outline of my thesisi) Let some "species" of concentration C(p), x 2 Rd, diuse stationary in the isotropic bulk from a (distant) source localised on the closed boundary $partial Omega_{0}$ towards a semipermeable compact interface $partial Omega$ of the cell $Omega in Omega_{0}$ where they disappear at a given rate $W >= 0$. Then the steady field of concentrations C satisfy the problem $(P1)$. (see the Thesis). We interest to solve (P1) in Twodimensional and Tridimensional cases and to calculate the local and total flux in order to solving the localisation inverse problem. In order to make easy the calculations, we take $Omega$ and $Omega_{0}$ with a regularly geometricals forms by distinguishing the two cases : Concentrics and non-concentrics case. For the non-cncentrics case, we use the conformal mapping technique for resolving the problem (P1) in the twodimensional case. whereas in the tridimensional case, we use the development according to the spherical harmonics functions.ii) Localisation inverse problemThe aim of the localisation inverse problem is to find the necessary Dirichlet-to-Neumann conditions in order to determine the position of thecell $Omega$, where these conditions are measurable.iii) Geometrical inverse problemOur main results concerns a formal solution of the geometrical inverse problem for the form of absorbing domains. We restrict this study to two dimensions and we study it by the conformal mapping technique and harmonic functions.iv) Dirichlet-to-Neumann operatorWe study the Dirichlet-to-Neumann operatot relative to problem (P1) in the twodimensional and tridimensionnal cases by distinguishing the two cases : Concentrics and non-concentrics case. We prove that the Dirichlet-to-Neumann operator generates some semi-group, we call it the Lax semi-group. Finally we construct this semi group and verify that this demi-group satisfies the generals properties of a operator
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Benson, A. "A new approach to the boundary integral method for the three dimensional Neumann problem." Thesis, University of Salford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356179.
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Pillay, Samara. "The narrow escape problem : a matched asymptotic expansion approach." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1428.
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We consider the motion of a Brownian particle trapped in an arbitrary bounded two or three-dimensional domain, whose boundary is reflecting except for a small absorbing window through which the particle can escape. We use the method of matched asymptotic expansions to calculate the mean first passage time, defined as the time taken for the Brownian particle to escape from the domain through the absorbing window. This is known as the narrow escape problem. Since the mean escape time diverges as the window shrinks, the calculation is a singular perturbation problem. We extend our results to include N absorbing windows of varying length in two dimensions and varying radius in three dimensions. We present findings in two dimensions for the unit disk, unit square and ellipse and in three dimensions for the unit sphere. The narrow escape problem has various applications in many fields including finance, biology, and statistical mechanics.
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Luna, Tito Luciano Mamani. "Bifurcação e estabilidade de equilíbrios de um problema de Neumann parabólico com peso indefinido em genética populacional." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/5914.
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Previous issue date: 2015-03-30<br>Financiadora de Estudos e Projetos<br>This work is concerned with a semilinear parabolic partial differential equation under a homogeneous Neumann boundary condition occuring in population genetics. It describes the evolution of gene frequencies under selection and migration effects in a bounded domain. In the nonlinear term appearing in the equation, which is of logistic type, one has a positive parameter and an indefinite sign weight function. Considering a suitable phase space one obtains a nonlinear dynamical system, actually a gradient system, in a such way that the equilibrium solutions, or stationary solutions, play a fundamental role in the dynamics viewpoint. The problem has two constant equilibria, called the trivial ones, inducing two curves, called trivial branches, and containing the trivial equilibrium solutions. The main aim of this dissertation is to study the bifurcation and stability structures of equilibria, which are completely established and also expressed through diagrams. Furthermore, to establish the behaviour of the only nontrivial equilibrium the problem has for each value of the parameter. A key ingredient in the analysis is the average of the weight function. Indeed, if the weight has nonzero average a global curve consisting of nontrivial exponentially stable equilibria bifurcates from a trivial branch − which is determined according to the sign of the average. But if the parameter is sufficiently small the problem admits the two trivial equilibria as the only equilibrium solutions, one of them exponentially stable and the other unstable. When the weight function has zero average a new curve has now a central role: from such curve bifurcates a global curve defined for all values of the parameter and consisting of nontrivial exponentially stable equilibria. Further, there is no bifurcation from the trivial branches, that ones containing unstable equilibria. Finally, the behaviour of the global bifurcation branch is also established as the parameter is large. Actually, that is achieved as long as one proves the only nontrivial equilibrium concentrates in a region where the weight function has a definite sign, as the parameter is large.<br>Neste trabalho estuda-se uma equação diferencial parcial parabólica semilinear com condição de fronteira de Neumann homogênea que surge em genética populacional, a qual descreve a evolução de frequências de genes sob a ação conjunta de migração e seleção numa regi ao limitada. No termo não-linear que aparece na equação, de tipo logístico, tem-se um parâmetro positivo e uma função peso de sinal indefinido. Considerando-se um espaço de fase adequado ao problema, determina-se um sistema dinâmico não-linear e gradiente, de forma que os equilíbrios, ou soluções estacionárias, desempenham um papel fundamental no que concerne a dinâmica. Há dois equilíbrios constantes, chamados triviais, que dão origem a duas curvas, chamadas ramos triviais, contendo os equilíbrios triviais. O objetivo principal desta dissertação é estudar as estruturas de bifurcação e estabilidade de todos os equilíbrios, as quais são completamente determinadas e expressas através de diagramas, além de determinar o comportamento do único equilíbrio não-trivial que o problema possui para cada valor do parâmetro. Elemento decisivo na análise é a média da função peso do termo não-linear. De fato, em caso de média não nula bifurca de ramo trivial − que é determinado pelo sinal da m´edia − uma curva global constituída de equilíbrios não-triviais exponencialmente estáveis, enquanto os únicos equilíbrios que podem existir quando o parâmetro é pequeno são os triviais, sendo um exponencialmente estável e outro instável. Quando a média da função peso é zero uma nova curva passa a ter papel central: dela bifurca uma curva global, definida para cada valor do parâmetro, constituída de equilíbrios não triviais exponencialmente estáveis e não há bifurcação dos ramos triviais, estes contendo então equilíbrios instáveis. Finalmente, é determinado o comportamento do ramo de bifurcação global quando o parâmetro é grande ao estabelecer-se que o único equilíbrio não trivial do problema tende a concentra-se numa região em que o peso tem sinal definido.
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Neumann, Fanny [Verfasser], and Klaus [Akademischer Betreuer] Püschel. "Sexueller Missbrauch von Kindern in Hamburg - ein Vergleich der Fälle aus den Jahren 2005 und 2009 / Fanny Neumann. Betreuer: Klaus Püschel." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2013. http://d-nb.info/1031280286/34.
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Isaev, Mikhail. "Stability and instability in inverse problems." Palaiseau, Ecole polytechnique, 2013. https://pastel.hal.science/docs/00/91/22/98/PDF/these.pdf.
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Dans cette thèse nous nous intéressons aux questions de stabilité et d'instabilité dans certains problèmes inverses classiques pour l'équation de Schrödinger et l'équation acoustique en dimension d>=2. Les problèmes considérés sont le problème inverse de Gel'fand de valeurs au bord et les problèmes inverses de diffusion en champ proche et en champ lointain. Les résultats de stabilité et d'instabilité présentés dans cette thèse se complètent mutuellement et contribuent à une meilleure compréhension de la nature des problèmes précités. En particulier, nous démontrons des nouvelles estimations de stabilité globale qui dépendent explicitement de la régularité du coefficient et de l'énergie. En outre, nous considérons le problème inverse de valeurs au bord pour l'équation de Schrödinger à l'énergie fixée avec des mesures frontières représentées comme l'opérateur frontière d'impédance (ou l'opérateur Robin-Robin). Nous démontrons des estimations de stabilité globale pour détermination du potentiel à partir de mesures frontières dans cette représentation d'impédance. De plus, des techniques similaires donnent aussi une procédure de reconstruction globale pour ce problème<br>In this thesis we focus on stability and instability issues in some classical inverse problems for the Schrödinger equation and the acoustic equation in dimension d>=2. The problems considered are the Gel'fand inverse boundary value problem, the nearfield and the far-field inverse scattering problems. Stability and instability results presented in the thesis complement each other and contribute to a better understanding of the nature of the aforementioned problems. In particular, we prove new global stability estimates which explicitly depend on coefficient regularity and energy. In addition, we consider the inverse boundary value problem for the Schrödinger equation at fixed energy with boundary measurements represented as the impedance boundary map (or Robin-to-Robin map). We prove global stability estimates for determining potential from boundary measurements in this impedance representation. Moreover, similar techniques also give a global reconstruction procedure for this problem
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Tarkhanov, Nikolai. "Harmonic integrals on domains with edges." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2680/.
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We study the Neumann problem for the de Rham complex in a bounded domain of Rn with singularities on the boundary. The singularities may be general enough, varying from Lipschitz domains to domains with cuspidal edges on the boundary. Following Lopatinskii we reduce the Neumann problem to a singular integral equation of the boundary. The Fredholm solvability of this equation is then equivalent to the Fredholm property of the Neumann problem in suitable function spaces. The boundary integral equation is explicitly written and may be treated in diverse methods. This way we obtain, in particular, asymptotic expansions of harmonic forms near singularities of the boundary.
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Nonvignon, Enock. "Probleme de neumann pour les equations de type monge-ampere sur certaines varietes riemaniennes compactes a bord." Paris 6, 1994. http://www.theses.fr/1994PA066212.
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Le but de cette these est de formuler quelques resultats relatifs a la generalisation aux varietes riemaniennes a bord du probleme de neumann pour les equations de type monge-ampere. A travers ce travail, nous utilisons le principe du maximum et la notion de repere adapte un systeme de coordonnees normales en un point p de la variete m ou la matrice hessienne d'une fonction lisse est diagonale. Au chapitre i, nous resolvons par la methode de continuite l'equation de monge-ampere dethess u=f dans m avec comme donnee de neumann a la frontiere ou f et sont des fonctions lisses et ou hess(u) designe la matrice hes sienne de u. Dans le chapitre suivant, nous resolvons l'equation de monge-ampere dont le second membre est lineaire en u (f+u,+'u) ou et ' sont positifs. Le chapitre iii est consacre a la resolution de l'equation de monge-ampere generale par la methode des sous et sur-solutions avec pour second membre f(x,u) ;(x,u). Les resultats de ce chapitre s'inspirent des travaux d'aubin sur le probleme de dirichlet correspondant dans un ouvert borne de l'espace euclidien de dimension n. Toutes les methodes dependent d'etablissement d'estimes a priori des derivees dans l'espace de holder d'exposant 2+ et conduisent a un resultat precis sur l'equation de la courbure de gauss prescrite
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Verfasser], Afzal, and Günter [Akademischer Betreuer] [Neumann. "Re-plant problems in long-term no-tillage cropping systems : causal analysis and mitigation strategies / Afzal ; Betreuer: Günter Neumann." Hohenheim : Kommunikations-, Informations- und Medienzentrum der Universität Hohenheim, 2017. http://d-nb.info/1142977625/34.
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Neumann, Laura [Verfasser]. "Die externe Qualitätssicherung im Krankenhausrecht : Im Spannungsfeld zwischen Patientenschutz, Trägerinteressen, Zielen der gesetzlichen Krankenversicherung und staatlicher Regulierung / Laura Neumann." Baden-Baden : Nomos Verlagsgesellschaft mbH & Co. KG, 2019. http://d-nb.info/1183473273/34.
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Konangi, Santosh. "Stability Analysis of Artificial-Compressibility-type and Pressure-Based Formulations for Various Discretization Schemes for 1-D and 2-D Inviscid Flow, with Verification Using Riemann Problem." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1321371661.
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Baker, Steven Jeffrey. "Spectral properties of displacement models." Birmingham, Ala. : University of Alabama at Birmingham, 2007. https://www.mhsl.uab.edu/dt/2007p/baker.pdf.
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Thesis (Ph. D.)--University of Alabama at Birmingham, 2007.<br>Additional advisors: Richard Brown, Ioulia Karpechina, Ryoichi Kawai, Boris Kunin. Description based on contents viewed Feb. 5, 2008; title from title screen. Includes bibliographical references (p. 73-75).
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Cekić, Mihajlo. "The Calderón problem for connections." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/267829.
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This thesis is concerned with the inverse problem of determining a unitary connection $A$ on a Hermitian vector bundle $E$ of rank $m$ over a compact Riemannian manifold $(M, g)$ from the Dirichlet-to-Neumann (DN) map $\Lambda_A$ of the associated connection Laplacian $d_A^*d_A$. The connection is to be determined up to a unitary gauge equivalence equal to the identity at the boundary. In our first approach to the problem, we restrict our attention to conformally transversally anisotropic (cylindrical) manifolds $M \Subset \mathbb{R}\times M_0$. Our strategy can be described as follows: we construct the special Complex Geometric Optics solutions oscillating in the vertical direction, that concentrate near geodesics and use their density in an integral identity to reduce the problem to a suitable $X$-ray transform on $M_0$. The construction is based on our proof of existence of Gaussian Beams on $M_0$, which are a family of smooth approximate solutions to $d_A^*d_Au = 0$ depending on a parameter $\tau \in \mathbb{R}$, bounded in $L^2$ norm and concentrating in measure along geodesics when $\tau \to \infty$, whereas the small remainder (that makes the solution exact) can be shown to exist by using suitable Carleman estimates. In the case $m = 1$, we prove the recovery of the connection given the injectivity of the $X$-ray transform on $0$ and $1$-forms on $M_0$. For $m > 1$ and $M_0$ simple we reduce the problem to a certain two dimensional $\textit{new non-abelian ray transform}$. In our second approach, we assume that the connection $A$ is a $\textit{Yang-Mills connection}$ and no additional assumption on $M$. We construct a global gauge for $A$ (possibly singular at some points) that ties well with the DN map and in which the Yang-Mills equations become elliptic. By using the unique continuation property for elliptic systems and the fact that the singular set is suitably small, we are able to propagate the gauges globally. For the case $m = 1$ we are able to reconstruct the connection, whereas for $m > 1$ we are forced to make the technical assumption that $(M, g)$ is analytic in order to prove the recovery. Finally, in both approaches we are using the vital fact that is proved in this work: $\Lambda_A$ is a pseudodifferential operator of order $1$ acting on sections of $E|_{\partial M}$, whose full symbol determines the full Taylor expansion of $A$ at the boundary.