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Dissertations / Theses on the topic 'Hölder and Sobolev spaces'

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Published: 4 June 2021

Last updated: 2 February 2022

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1

Karlsson, John. "Lebesgue points, Hölder continuity and Sobolev functions." Thesis, Linköping University, Linköping University, Linköping University, Department of Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-16759.

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<p>This paper deals with Lebesgue points and studies properties of the set of Lebesgue points for various classes of functions. We consider continuous functions, L<sup>1</sup> functions and Sobolev functions. In the case of uniformly continuous functions and Hölder continuous functions we develop a characterization in terms of Lebesgue points. For Sobolev functions we study the dimension of the set of non-Lebesgue points.</p>

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2

Salloum, Zaynab. "Étude mathématique d’écoulements de fluides viscoélastiques dans des domaines singuliers." Thesis, Paris Est, 2008. http://www.theses.fr/2008PEST0017/document.

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Cette thèse est consacrée à l’analyse mathématique de trois problèmes d’écoulements de fluides viscoélastiques de type Oldroyd. Tout d’abord, nous étudions des écoulements stationnaires faiblement compressibles dans un domaine borné avec des conditions au bord de type "rentrante-sortante". Nous étudions aussi le problème d’écoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une méthode de point fixe (premier et deuxième problèmes) et une décomposition de Helmoltz (deuxième problème), nous montrons des résultats d’existence et d’unicité des solutions. Nous étud

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3

Nguyen, Hoang Phuong. "Résultats de compacité et régularité dans un modèle de Ginzburg-Landau non-local issu du micromagnétisme. Lemme de Poincaré et régularité du domaine." Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30315.

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Dans cette thèse, nous étudions des problèmes aux limites impliquant le modèle micro-magnétique et les formes différentielles. Dans la première partie, nous considérons un modèle non-local de Ginzburg-Landau apparaissant en micromagnétisme avec une condition au bord de type Dirichlet. Le modèle typique implique une fonctionelle d'énergie définie pour des applications des valeurs dans la sphère S² et qui depend de plusieurs paramètres, qui représentent des quantités physiques. Une première question concerne la compacité des aimantations ayant les énergies de quelques parois de Néel de longueur

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4

Clemens, Jason. "Sobolev spaces." Kansas State University, 2014. http://hdl.handle.net/2097/18186.

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Master of Science<br>Department of Mathematics<br>Marianne Korten<br>The goal for this paper is to present material from Gilbarg and Trudinger’s Elliptic Partial Differential Equations of Second Order chapter 7 on Sobolev spaces, in a manner easily accessible to a beginning graduate student. The properties of weak derivatives and there relationship to conventional concepts from calculus are the main focus, that is when do weak and strong derivatives coincide. To enable the progression into the primary focus, the process of mollification is presented and is widely used in estimations. Imbeddin

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5

Färm, David. "Upper gradients and Sobolev spaces on metric spaces." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5816.

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<p>The Laplace equation and the related p-Laplace equation are closely associated with Sobolev spaces. During the last 15 years people have been exploring the possibility of solving partial differential equations in general metric spaces by generalizing the concept of Sobolev spaces. One such generalization is the Newtonian space where one uses upper gradients to compensate for the lack of a derivative.</p><p>All papers on this topic are written for an audience of fellow researchers and people with graduate level mathematical skills. In this thesis we give an introduction to the Newtonian spac

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6

Park, Young Ja. "Sobolev trace inequality and logarithmic Sobolev trace inequality." Digital version:, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p9992883.

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7

Spector, Daniel. "Characterization of Sobolev and BV Spaces." Research Showcase @ CMU, 2011. http://repository.cmu.edu/dissertations/78.

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This work presents some new characterizations of Sobolev spaces and the space of functions of Bounded Variation. Additionally it gives new proofs of continuity and lower semicontinuity theorems due to Reshetnyak.

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8

Neves, Julio Severino. "Fractional Sobolev-type spaces and embeddings." Thesis, University of Sussex, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341514.

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9

Dines, Nicoleta, Gohar Harutjunjan, and Bert-Wolfgang Schulze. "The Zaremba problem in edge Sobolev spaces." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2661/.

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Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.

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10

Gjestland, Fredrik Joachim. "Distributions, Schwartz Space and Fractional Sobolev Spaces." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-23452.

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This thesis derives the theory of distributions, starting with test functions as a basis. Distributions and their derivatives will be analysed and exemplified. Schwartz functions are introduced, and the Fourier transform of Schwartz functions is analysed, creating the basis for Tempered distributions on which we also analyse the Fourier transform. Weak derivatives and Sobolev spaces are defined, and from the Fourier transform we define Sobolev spaces of non-integer order. The theory presented is applied to an initial value problem with a derivative of order one in time and an arbitrary differe

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11

Davidsson, Johan. "Sobolev Spaces and the Finite Element Method." Thesis, Örebro universitet, Institutionen för naturvetenskap och teknik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-67470.

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In this essay we present the Sobolev spaces and some basic properties of them. The Sobolev spaces serve as a theoretical framework for studying solutions to partial differential equations. The finite element method is presented which is a numerical method for solving partial differential equations.

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12

Clavero, Nadia F. "Optimal Sobolev Embeddings in Spaces with Mixed Norm." Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/292613.

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Este proyecto hace referencia a estimaciones, en espacios funcionales, que relacionan la norma de una función y la de sus derivadas. Concretamente, nuestro principal objetivo es estudiar las estimaciones clásicas de las inclusiones de Sobolev, probadas por Gagliardo y Nirenberg, para derivadas de orden superior y espacios más generales. En particular, estamos interesados en describir el dominio y el rango óptimos para estas inclusiones entre los espacios invariantes por reordenamiento (r.i.) y espacios de normas mixtas.<br>This thesis project concerns estimates, in function spaces, that relate

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13

Flucher, Martin. "Concentration and compactness of functionals on Sobolev spaces /." [S.l.] : [s.n.], 1991. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=9525.

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14

Mekias, Mohamed. "Restriction to hypersurfaces of non-isotropic Sobolev spaces." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/100868.

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15

Airapetyan, Ruben, and Ingo Witt. "Isometric properties of the Hankel Transformation in weighted sobolev spaces." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2500/.

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It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inver

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16

Döhring, Nicolas [Verfasser]. "Regularity of Random Fields in Scales of Besov Spaces and Generalized Sobolev Spaces / Nicolas Döhring." München : Verlag Dr. Hut, 2016. http://d-nb.info/1084386887/34.

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17

Georgoulis, Emmanuil H. "Discontinuous Galerkin methods on shape-regular and anisotropic meshes." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270366.

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18

Inahama, Yuzuru. "Logarithmic Sobolev Inequality on Free Loop Groups for Heat Ker-nel Measures Associated with the General Sobolev Spaces." 京都大学 (Kyoto University), 2001. http://hdl.handle.net/2433/150808.

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19

Malý, Lukáš. "Sobolev-Type Spaces : Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces." Doctoral thesis, Linköpings universitet, Matematik och tillämpad matematik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-105616.

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This thesis consists of four papers and focuses on function spaces related to first-order analysis in abstract metric measure spaces. The classical (i.e., Sobolev) theory in Euclidean spaces makes use of summability of distributional gradients, whose definition depends on the linear structure of Rn. In metric spaces, we can replace the distributional gradients by (weak) upper gradients that control the functions’ behavior along (almost) all rectifiable curves, which gives rise to the so-called Newtonian spaces. The summability condition, considered in the thesis, is expressed using a general B

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20

Blair, Matthew D. "Strichartz estimates for wave equations with coefficients of Sobolev regularity /." Thesis, Connect to this title online; UW restricted, 2005. http://hdl.handle.net/1773/5745.

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21

Silvestre, Albero María Pilar. "Capacitary function spaces and applications." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/77717.

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The first part of the thesis is devoted to the analysis on a capacity space, with capacities as substitutes of measures in the study of function spaces. The goal is to extend to the associated function lattices some aspects of the theory of Banach function spaces, to show how the general theory can be applied to classical function spaces such as Lorentz spaces, and to complete the real interpolation theory for these spaces included in [CeClM] and [Ce]. In the second part of the thesis, we present an integral inequality connecting a function space norm of the gradient of a function to an int

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22

Schrohe, Elmar, and Jörg Seiler. "Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2562/.

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Given a manifold B with conical singularities, we consider the cone algebra with discrete asymptotics, introduced by Schulze, on a suitable scale of Lp-Sobolev spaces. Ellipticity is proven to be equivalent to the Fredholm property in these spaces, it turns out to be independent of the choice of p. We then show that the cone algebra is closed under inversion: whenever an operator is invertible between the associated Sobolev spaces, its inverse belongs to the calculus. We use these results to analyze the behaviour of these operators on Lp(B).

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23

Prats, Soler Martí. "Singular integral operators on sobolev spaces on domains and quasiconformal mappings." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/314193.

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En aquesta tesi s’obtenen nous resultats sobre l’acotació d’operadors de Calderón-Zygmund en espais de Sobolev en dominis de Rd. En primer lloc es demostra un teorema de tipus T(P) vàlid per a Wn,p(U), a on U és un domini uniforme acotat de Rd, n és un nombre natural arbitrari, i p>d. Essencialment, el resultat obtingut afirma que un operador de Calderón-Zygmund de convolució és acotat en aquest espai si i solament si per a tot polinomi P de grau menor que n restringit al domini, T(P) pertany a Wn,p(U). Per a índexs p menors o iguals que d, es demostra una condició suficient per a l'acotac

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24

Buffa, Vito. "Higher order Sobolev Spaces and polyharmonic boundary value problems in Carnot Groups." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6893/.

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The main task of this work is to present a concise survey on the theory of certain function spaces in the contexts of Hörmander vector fields and Carnot Groups, and to discuss briefly an application to some polyharmonic boundary value problems on Carnot Groups of step 2.

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25

Khanfar, Abeer. "Multiple Solutions on a Ball for a Generalized Lane Emden Equation." ScholarWorks@UNO, 2008. http://scholarworks.uno.edu/td/901.

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In this work we study the Generalized Lane-Emden equation and the interplay between the exponents involved and their consequences on the existence and non existence of radial solutions on a unit ball in n dimensions. We extend the analysis to the phase plane for a clear understanding of the behavior of solutions and the relationship between their existence and the growth of nonlinear terms, where we investigate the critical exponent p and a sub-critical exponent, which we refer to as ^p. We discover a structural change of solutions due the existence of this sub-critical exponent which we relat

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26

Arden, Greg. "Approximation properties of subdivision surfaces /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/5765.

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27

Mahavier, William Ted. "A Numerical Method for Solving Singular Differential Equations Utilizing Steepest Descent in Weighted Sobolev Spaces." Thesis, University of North Texas, 1995. https://digital.library.unt.edu/ark:/67531/metadc278653/.

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We develop a numerical method for solving singular differential equations and demonstrate the method on a variety of singular problems including first order ordinary differential equations, second order ordinary differential equations which have variational principles, and one partial differential equation.

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28

Ortiz, Vargas Walter Andrés. "Sobolev inequalities: isoperimetry and symmetrization." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/669904.

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29

Algervik, Robert. "Embedding Theorems for Mixed Norm Spaces and Applications." Licentiate thesis, Karlstad : Faculty of Technology and Science, Mathematics, Karlstads universitet, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-2874.

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30

Tami, Abdelkader. "Etude d'un problème pour le bilaplacien dans une famille d'ouverts du plan." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4362/document.

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L’objet de cette thèse est l’étude du problème Δ 2uω = fω avec les conditions aux limites Uω = Δ uω = 0, le second membre étant supposé dépendre continûment de ω dans L2(ω), où ω = {(r, θ); 0 < r < 1, 0 < θ < ω} , 0 < ω ≤ π, est une famille de secteurs tronqués du plan. Si ω < π on sait d’après Blum et Rannacher (1980) que la solution de ce problème uω se décompose au voisinage de l’origine en uω = u1,ω + u2,ω + u3,ω, (1) où u1,ω, u2,ω sont les parties singulières de uω et u3,ω la partie régulière. En effet, au voisinage de l’origine u1,ω (resp. u2,ω, u3,ω) est de régularité

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31

Brewster, Kevin. "Surface to surface changes of variables and applications." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5759.

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Thesis (Masters of Science for Teachers)--University of Missouri-Columbia, 2008.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 25, 2008) Vita. Includes bibliographical references.

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32

Bento, Antonio Jorge Gomes. "Interpolation, measures of non-compactness, entropy numbers and s-numbers." Thesis, University of Sussex, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.344067.

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33

Bihun, Oksana Chicone Carmen Charles. "Approximate isometries and distortion energy functionals." Diss., Columbia, Mo. : University of Missouri--Columbia, 2009. http://hdl.handle.net/10355/6129.

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Title from PDF of title page (University of Missouri--Columbia, viewed on Feb. 11, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Professor Carmen Chicone. Vita. Includes bibliographical references.

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34

Oliveira, Andrielber da Silva. "Metodos de interpolação real e espaços de Sobolev e Besov sobre a esfera Sd." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306560.

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Orientador: Sergio Antonio Tozoni<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-06T13:07:08Z (GMT). No. of bitstreams: 1 Oliveira_AndrielberdaSilva_M.pdf: 1284065 bytes, checksum: 0117263cf98921db674e49f5f57d460d (MD5) Previous issue date: 2006<br>Resumo: O objetivo da dissertação é realizar um estudo dos espaços de Besov sobre a esfera unitária d-dimensional real Sd. No primeiro capítulo são estudados espaços de interpolação utilizando dois métodos de interpolação real. Em pa

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35

Bruder, Andrea S. Littlejohn Lance L. "Applied left-definite theory the Jacobi polynomials, their Sobolev orthogonality, and self-adjoint operators /." Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5327.

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Thesis (Ph.D.)--Baylor University, 2009.<br>Subscript in abstract: n and n=0 in {Pn([alpha],[beta])(x)} [infinity] n=0, [mu] in (f,g)[mu], and R in [integral]Rfgd[mu]. Superscript in abstract: ([alpha],[beta]) and [infinity] in {Pn([alpha],[beta])(x)} [infinity] n=0. Includes bibliographical references (p. 115-119).

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36

McCabe, Terence W. (Terence William). "Minimization of a Nonlinear Elasticity Functional Using Steepest Descent." Thesis, University of North Texas, 1988. https://digital.library.unt.edu/ark:/67531/metadc331296/.

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37

Bandyopadhyay, Jogia. "Optimal concentration for SU(1,1) coherent state transforms and an analogue of the Lieb-Wehrl conjecture for SU(1,1)." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24801.

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Thesis (Ph.D.)--Physics, Georgia Institute of Technology, 2008.<br>Committee Chair: Eric A. Carlen; Committee Member: Jean Bellissard; Committee Member: Michael Loss; Committee Member: Predrag Cvitanovic.

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38

Chappa, Eduardo. "The x-ray transform of tensor fields /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/5750.

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39

Medeiros, Luiz Adauto, and Juan Límaco. "On the Kirchhoff equation in noncylindrical domains of R." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97270.

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40

Sloane, Craig Andrew. "Hardy-Sobolev-Maz'ya inequalities for fractional integrals on halfspaces and convex domains." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/41125.

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This thesis will present new results involving Hardy and Hardy-Sobolev-Maz'ya inequalities for fractional integrals. There are two key ingredients to many of these results. The first is the conformal transformation between the upper halfspace and the unit ball. The second is the pseudosymmetric halfspace rearrangement, which is a type of rearrangment on the upper halfspace based on Carlen and Loss' concept of competing symmetries along with certain geometric considerations from the conformal transformation. After reducing to one dimension, we can use the conformal transformation to prove a sh

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41

Dima, Ute [Verfasser], and Arnd [Akademischer Betreuer] Rösch. "Regularization in fractional order Sobolev spaces for a parameter identification problem / Ute Dima ; Betreuer: Arnd Rösch." Duisburg, 2017. http://d-nb.info/1147681287/34.

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42

Algervik, Robert. "Embedding Theorems for Mixed Norm Spaces and Applications." Doctoral thesis, Karlstads universitet, Avdelningen för matematik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-5646.

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This thesis is devoted to the study of mixed norm spaces that arise in connection with embeddings of Sobolev and Besov type spaces. We study different structural, integrability, and smoothness properties of functions satisfying certain mixed norm conditions. Conditions of this type are determined by the behaviour of linear sections of functions. The work in this direction originates in a paper due to Gagliardo (1958), and was further developed by Fournier (1988), by Blei and Fournier (1989), and by Kolyada (2005). Here we continue these studies. We obtain some refinements of known embeddings f

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43

Brauer, Uwe, and Lavi Karp. "Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3017/.

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We prove the existence of a class of local in time solutions, including static solutions, of the Einstein-Euler system. This result is the relativistic generalisation of a similar result for the Euler-Poisson system obtained by Gamblin [8]. As in his case the initial data of the density do not have compact support but fall off at infinity in an appropriate manner. An essential tool in our approach is the construction and use of weighted Sobolev spaces of fractional order. Moreover, these new spaces allow us to improve the regularity conditions for the solutions of evolution equations. The deta

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44

Gonçalves, Breno Lucas da Costa. "An introduction to distribution theory, Fourier transform, Sobolev spaces and its applications to the Black-Scholes Equation." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/19247.

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Mestrado em Mathematical Finance<br>A maior parte da teoria citada em cursos introdutórios de análise matemática e cálculo foi elaborada ainda antes do século XVIII. No entanto, em meados de 1950, Laurent Schwartz desenvolveu um novo conceito que mudou e redefiniu a noção de função. A definição de derivada e transformada de Fourier são dois dos conceitos mais importantes em análise e essenciais para o estudo de equações diferenciais parciais. No entanto, note-se que nem todas as funções são diferenciáveis ou possuem uma transformada de Fourier. A teoria de distribuições permite esta correção

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45

Wolf, Jörg. "Regularität schwacher Lösungen nichtlinearer elliptischer und parabolischer Systeme partieller Differentialgleichungen mit Entartung." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14792.

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In der vorliegenden Arbeit untersuchen wir schwache Lösungen, die zu einem geeigneten Sobolevraum gehören, q-elliptischer und parabolischer Systeme partieller Differentialgleichungen auf deren Regularität für den Fall 1<br>In the present work we study the regularity of weak solution to q-elliptic and parabolic systems partial differential equations in appropriate Sobolev spaces in case 1

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46

Silva, Rômel da Rosa da. "O problema de Cauchy para sistemas quase-lineares hiperbólicos é bem posto em espaços de Hölder." Universidade Federal de São Carlos, 2012. https://repositorio.ufscar.br/handle/ufscar/5828.

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Made available in DSpace on 2016-06-02T20:27:40Z (GMT). No. of bitstreams: 1 4444.pdf: 689745 bytes, checksum: 511f734e8913b3b1285fcda6fb0c67e3 (MD5) Previous issue date: 2012-08-10<br>Financiadora de Estudos e Projetos<br>We consider the Cauchy problem for the quasi-linear systems that is, the system is hyperbolic at u = 0. We show that certain Besov spaces are preserved by flow of the solution, near the null solution.<br>Nós consideramos o problema de Cauchy para sistemas quase-lineares, ou seja o sistema é hiperbólico em u = 0. Demonstramos que certos espaços de Besov são preservados pelo

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47

Roth, John Charles. "Perturbations of Kähler-Einstein metrics /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5737.

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48

Benetti, Francesco. "The Cauchy problem for the wave equation." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18369/.

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In questo lavoro viene esposta la teoria del problema di Cauchy per l'equazione delle onde in un mezzo omogeneo e isotropo in dimensione qualunque. I primi due capitoli sono incentrati sull'approcio classico alla soluzione del problema. In particolare, nel primo capitolo si studia il problema in tutto lo spazio, mentre nel secondo in un dominio limitato, con condizioni al contorno. Nel terzo capitolo viene esposta la teoria degli Spazi di Sobolev, che verrà poi applicata nel capitolo successivo, nella cosiddetta formulazione debole del problema. L'ultimo capitolo è dedicato alle applicazion

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Santiago, Landerson Bezerra. "O nÃcleo do calor em uma variedade riemanniana." Universidade Federal do CearÃ, 2011. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5674.

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Abstract:

Em uma variedade riemanniana conexa e compacta introduziremos o conceito de espectro do operador laplaciano. Utilizando a existÃncia e a unicidade do nÃcleo do calor em uma variedade riemanniana,provaremos o teorema de decomposiÃÃo de Hodge. Este teorema afirma que o espaÃo de Hilbert L2(M, g) se decompÃe em uma soma direta de subespaÃos de dimensÃo finita, onde cada subespaÃo Ã o auto-espaÃo associado a um autovalor do laplaciano. AlÃm disso, os autovalores formam uma sequÃncia nÃo-negativa que acumula somente no infinito. Em seguida iniciaremos a construÃÃo do nÃcleo do calor e, por fim, mos

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Montealegre, Scott Juan. "Initial value problem for a coupled system of Kadomtsev-Petviashvili II equations in Sobolev spaces of negative indices." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95255.

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