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Dissertations / Theses on the topic 'Singular integral operator'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Bosch, Camós Anna. "Controlant la integral singular maximal." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/314177.

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Els principals objectes d'estudi d'aquesta memòria són les integrals singulars. Per l'elaboració d'aquesta memòria, trobem una especial motivació en tres articles originats a partir de la idea d'acotar la norma de l'operador maximal d'una integral singular per la norma de la integral singular. En el primer article, de J. Mateu i J. Verdera del 2006, [MV], s'hi proven desigualtats puntuals pels casos particulars de la j-èssima transformada de Riesz i de la transformada de Beurling. Es fa notar per primer cop que les acotacions són diferents degut a la paritat del nucli de les respectives tran

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2

Chunaev, Petr. "Singular integral operators and rectifiability." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/663827.

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Los problemas que estudiamos en esta tesis se encuentran en el área de Análisis Armónico y Teoría de la Medida Geométrica. En particular, consideramos la conexión entre las propiedades analíticas de operadores integrales singulares definidos en $L^2(\mu)$ y asociados con algunos núcleos de Calderón-Zygmund y las propiedades geométricas de la medida $\mu$. Seamos más precisos. Sea $E$ un conjunto de Borel en el plano complejo con la medida lineal de Hausdorff $H^1$ finita y distinta de cero, es decir, $0<H^1(E)<\infty $. G. David y J.C. Léger (1999) probaron que el núcleo de Cauchy $1/z$ (e su

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3

Moussai, Madani. "Continuite de certains operateurs integraux singuliers sur les espaces de besov." Paris 7, 1987. http://www.theses.fr/1987PA077016.

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On s'interesse a des conditions necessaires et suffisantes de continuite-l**(2) (resp. Continuite - besov b**(s)::(p,q)), des commutateurs entre les operateurs pseudo-differentiels o. P. D. De type s**(11,a); a1 (resp. S**(11,0)), et les fonctions dont les gradients sont bornes (resp. Des multiplicateurs de besov m(b**(s)::(p,q))). La continuite - besov du commutateur a l'aide du critere de lemarie, mene a etudier la continuite des o. P. D. De type s**(01,0) sur m(b**(sp,q)): les o. P. D. D'ordre 0 sont bornes sur les versions "localisees l**(e") de b**(s)::(p,q), par consequent sur m(b**(s)::

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4

Li, Xiaochun. "Uniform bounds for the bilinear Hilbert transforms /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025634.

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5

Ehrhardt, Torsten. "Factorization theory for Toeplitz plus Hankel operators and singular integral operators with flip." Doctoral thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972573305.

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6

Hofmann, Bernd, and Wolfersdorf Lothar von. "New results on the degree of ill-posedness for integration operators with weights." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800545.

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We extend our results on the degree of ill-posedness for linear integration opera- tors A with weights mapping in the Hilbert space L^2(0,1), which were published in the journal 'Inverse Problems' in 2005 ([5]). Now we can prove that the degree one also holds for a family of exponential weight functions. In this context, we empha- size that for integration operators with outer weights the use of the operator AA^* is more appropriate for the analysis of eigenvalue problems and the corresponding asymptotics of singular values than the former use of A^*A.

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7

Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.

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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwells equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission pro

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8

Vaktnäs, Marcus. "On Singular Integral Operators." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-355872.

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9

Reguera, Rodriguez Maria del Carmen. "Sharp weighted estimates for singular integral operators." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39522.

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The thesis provides answers, in one case partial and in the other final, to two conjectures in the area of weighted inequalities for Singular Integral Operators. We study the mapping properties of these operators in weighted Lebesgue spaces with weight w. The novelty of this thesis resides in proving sharp dependence of the operator norm on the Muckenhoupt constant associated to the weigth w for a rich class of Singular Integral operators. The thesis also addresses the end point case p=1, providing counterexamples for the dyadic and continuous settings.

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10

Santana, Edixon Manuel Rojas. "A study of singular integral operators with shift." Doctoral thesis, Universidade de Aveiro, 2010. http://hdl.handle.net/10773/3882.

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Doutoramento em Matemática<br>Nesta tese, consideram-se operadores integrais singulares com a acção extra de um operador de deslocacamento de Carleman e com coeficientes em diferentes classes de funções essencialmente limitadas. Nomeadamente, funções contínuas por troços, funções quase-periódicas e funções possuíndo factorização generalizada. Nos casos dos operadores integrais singulares com deslocamento dado pelo operador de reflexão ou pelo operador de salto no círculo unitário complexo, obtêm-se critérios para a propriedade de Fredholm. Para os coeficientes contínuos, uma fórmula do

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11

Vähäkangas, Antti V. "Boundedness of weakly singular integral operators on domains /." Helsinki : Suomalainen Tiedeakatemia, 2009. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018603140&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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12

Kaiser, Robert. "Polynomiale Kollokations-Quadraturverfahren für singuläre Integralgleichungen mit festen Singularitäten." Doctoral thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-229930.

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Viele Probleme der Riss- und Bruchmechanik sowie der mathematischen Physik lassen sich auf Lösungen von singulären Integralgleichungen über einem Intervall zurückführen. Diese Gleichungen setzen sich im Wesentlichen aus dem Cauchy'schen singulären Integraloperator und zusätzlichen Integraloperatoren mit festen Singularitäten in den jeweiligen Kernen zusammen. Zur numerischen Lösung solcher Gleichungen werden polynomiale Kollokations-Quadraturverfahren betrachet. Als Ansatzfunktionen und Kollokationspunkte werden dabei gewichtete Polynome und Tschebyscheff-Knoten gewählt. Die Gewichte sind so g

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13

Monguzzi, A. "ON THE REGULARITY OF SINGULAR INTEGRAL OPERATORS ON COMPLEX DOMAINS." Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/269875.

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Given a doman $\Omega$ in $C^n$, it is a classical problem to study the boundary behavior of functions which are holomorphic on $\Omega$. The boundary values of a given function are often expressed by means of singular integral operators. In this thesis we study this problem in two different settings with different motivations. In the first part we deal with a non-smooth version of the so-called worm domain in order to understand the role played by the pathological geometry of this domain. In the second part we study the problem in the case of a product Lipschitz surface and some boundedness r

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14

Haese-Hill, William. "Spectral properties of integrable Schrodinger operators with singular potentials." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/19929.

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The integrable Schrödinger operators often have a singularity on the real line, which creates problems for their spectral analysis. In several particular cases we show that all closed gaps lie on the infinite spectral arc. In the second part we develop a theory of complex exceptional orthogonal polynomials corresponding to integrable rational and trigonometric Schrödinger operators, which may have a singularity on the real line. In particular, we study the properties of the corresponding complex exceptional Hermite polynomials related to Darboux transformations of the harmonic oscillator, an

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15

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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16

Assaad, Joyce. "Transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels négatifs." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14106/document.

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Dans cette thèse nous étudions la bornitude des transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels qui admettent des parties négatives.Cette étude a lieu dans un premier temps sur les espaces de Lebesgue Lp(RN, dx), puissur les espaces Lp(M, dx) où M est une variété Riemannienne de type homogène et dans un dernier temps sur les espaces à poids Lp(RN,wdx). Nous considérons également,sur ces espaces à poids, la bornitude du calcul fonctionnel holomorphe associé et la bornitude des puissances négatives de l’opérateur de Schrödinger<br>In this thesis we study the bou

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17

Bennett, Jonathan Mark. "Oscillatory singular integrals with variable flat phases, and related operators." Thesis, University of Edinburgh, 1999. http://hdl.handle.net/1842/14028.

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18

Castro, Mario Henrique de. "Decaimento dos autovalores de operadores integrais positivos gerados por núcleos Laplace-Beltrami diferenciáveis." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-14092011-094712/.

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Neste trabalho obtemos taxas de decaimento para autovalores e valores singulares de operadores integrais gerados por núcleos de quadrado integrável sobre a esfera unitária em \'R POT. m+1\', m 2, sob hipóteses sobre ambos, certas derivadas do núcleo e o operador integral gerado por tais derivadas. Este tipo de problema é comum na literatura, mas as hipóteses geralmente são definidas via diferenciação usual em \'R POT m+1\'. Aqui, as hipóteses são todas definidas via derivada de Laplace-Beltrami, um conceito genuinamente esférico investigado primeiramente por W. Rudin no começo dos anos 50. As

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19

Awala, Hussein. "SINGULAR INTEGRAL OPERATORS ASSOCIATED WITH ELLIPTIC BOUNDARY VALUE PROBLEMS IN NON-SMOOTH DOMAINS." Diss., Temple University Libraries, 2017. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/453799.

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Mathematics<br>Ph.D.<br>Many boundary value problems of mathematical physics are modelled by elliptic differential operators L in a given domain Ω . An effective method for treating such problems is the method of layer potentials, whose essence resides in reducing matters to solving a boundary integral equation. This, in turn, requires inverting a singular integral operator, naturally associated with L and Ω, on appropriate function spaces on ƌΩ. When the operator L is of second order and the domain Ω is Lipschitz (i.e., Ω is locally the upper-graph of a Lipschitz function) the fundame

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20

Prado, Roxana Bedoya. "Operadores de Calderón-Zygmund e o teorema T1." Universidade Federal de São Carlos, 2009. https://repositorio.ufscar.br/handle/ufscar/5862.

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Made available in DSpace on 2016-06-02T20:28:24Z (GMT). No. of bitstreams: 1 2583.pdf: 836539 bytes, checksum: e0a45d9823e5681bd14db3b57f2cdf99 (MD5) Previous issue date: 2009-04-14<br>Financiadora de Estudos e Projetos<br>In this work, we present necessary and suficient conditions for that an operator of Calderón-Zygmund type can be extended to a bounded operator on L2. By using results of interpolation and cancellation conditions on the kernel to obtain the boundeness in Lp, for all 1 < p < 1.<br>Neste trabalho, apresentamos condições necessárias e suficientes para que um operador de tipo

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21

Roos, Joris [Verfasser]. "Singular integrals and maximal operators related to Carleson's theorem and curves in the plane / Joris Roos." Bonn : Universitäts- und Landesbibliothek Bonn, 2017. http://d-nb.info/1139049038/34.

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22

VOLPI, SARA MARIA. "Bochner-riesz means of eigenfunction expansions and local hardy spaces on manifolds with bounded geometry." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2012. http://hdl.handle.net/10281/29105.

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The thesis deals with two quite different problems: the first is the pointwise convergence of Bochner-Riesz means of functions with some smoothness and the Hausdorff dimension of the divergence set, the second is the development of new Hardy type spaces in order to obtain endpoint estimates for singular integral operators releted to the Laplace-Beltrami operator on Riemannian manifolds.

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23

Aksoy, Umit. "Schwarz Problem For Complex Partial Differential Equations." Phd thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607977/index.pdf.

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This study consists of four chapters. In the first chapter we give some historical background of the problem, basic definitions and properties. Basic integral operators of complex analysis and and Schwarz problem for model equations are presented in Chapter 2. Chapter 3 is devoted to the investigation of the properties of a class of strongly singular integral operators. In the last chapter we consider the Schwarz boundary value problem for the general partial complex differential equations of higher order.

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24

LY, KIM HA. "ON TWO APPROACHES FOR PARTIAL DIFFERENTIAL EQUATIONS IN SEVERAL COMPLEX VARIABLES." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423534.

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The aim of this thesis is to present influence of notations of ''type" on partial differential equations in several complex variables. The notations of "type" here include the finite and the infinite type in the sense of Hormander, and D'Angelo. In particular, in the first part, under the finite type condition, we will consider the existence and uniqueness of solutions for the initial value problem associated to the heat operator δs+□b on CR manifolds. The finite type m is the critical condition to provide pointwise estimates of the heat kernel via theory of singular integral operators develop

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25

Hou, Hedong. "Boundedness of operators on tent spaces and applications to PDE's." Electronic Thesis or Diss., université Paris-Saclay, 2025. http://www.theses.fr/2025UPASM020.

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Cette thèse étudie la continuité des opérateurs d'intégrale singulière sur les espaces de tentes et explore leurs applications aux EDP paraboliques. Nous développons un cadre théorique fondé sur la décroissance hors-diagonale. Ce cadre fournit un résultat amélioré (éventuellement optimal) concernant la continuité de l'opérateur de régularité maximale sur ces espaces. En nous appuyant sur ce cadre, nous établissons un panorama complet concernant l'existence, l'unicité et la représentation des solutions faibles aux problèmes de Cauchy paraboliques non-autonomes sous forme divergence. Les coeffic

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26

Routin, Eddy. "Local Tb theorems and Hardy type inequalities." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00656023.

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In this thesis, we study local Tb theorems for singular integral operators in the setting of spaces of homogeneous type. We give a direct proof of the local Tb theorem with L^2 integrability on the pseudo- accretive system. Our argument relies on the Beylkin-Coifman-Rokhlin algorithm applied in adapted Haar wavelet basis and some stopping time results. Motivated by questions of S. Hofmann, we extend it to the case when the integrability conditions are lower than 2, with an additional weak boundedness type hypothesis, which incorporates some Hardy type inequalities. We study the possibility of

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27

Huang, Yi. "Théorie des opérateurs sur les espaces de tentes." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS100/document.

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Nous donnons un mécanisme de type Calderón-Zygmund concernant la théorie de l’extrapolationpour des opérateurs d’intégrale singulière sur les espaces de tentes. Pour des opérateursde régularité maximale sur les espaces de tentes, nous donnons des résultats optimaux enexploitant la structure des opérateurs intégraux de convolution et en utilisant des estimationsde la décroissance hors-diagonale du semi-groupe ou de la famille résolvante sous-jacente.Nous appliquons des techniques précédentes d’analyse harmonique et fonctionnelle pourestimer sur les espaces de tentes certains opérateurs d’intégr

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28

Su, Yee-Ying, and 蘇奕穎. "An Example of the Monge-Ampère Singular Integral Operator." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/5utbm4.

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碩士<br>國立中央大學<br>數學系<br>104<br>Let ϕ(x) = x2 be a strictly convex and smooth function on R, we construct Sϕ(x, t) = B(x, √t), where B(x, √t) is a open interval with center x and radius √t. Then the section Sϕ satisﬁes the condition of section. we also construct an example of the Monge-Ap`ere singular integral operator.

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29

"Wavelets and singular integral operators." 1999. http://library.cuhk.edu.hk/record=b5889903.

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by Lau Shui-kong, Francis.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.<br>Includes bibliographical references (leaves 95-98).<br>Abstracts in English and Chinese.<br>Chapter 1 --- General Theory of Wavelets --- p.8<br>Chapter 1.1 --- Introduction --- p.8<br>Chapter 1.2 --- Multiresolution Analysis and Wavelets --- p.9<br>Chapter 1.3 --- Orthonormal Bases of Compactly Supported Wavelets --- p.12<br>Chapter 1.3.1 --- Example : The Daubechies Wavelets --- p.15<br>Chapter 1.4 --- Wavelets in Higher Dimensions --- p.20<br>Chapter 1.4.1 --- Tensor product method --- p.20<br>Ch

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30

"Singular integral operators on amalgam spaces." 2004. http://library.cuhk.edu.hk/record=b6073635.

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by Hon-Ming Ho.<br>"May 2004."<br>Thesis (Ph.D.)--Chinese University of Hong Kong, 2004.<br>Includes bibliographical references (p. 69-71).<br>Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.<br>Mode of access: World Wide Web.<br>Abstracts in English and Chinese.

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31

Axelsson, Andreas. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." Phd thesis, 2002. http://hdl.handle.net/1885/46056.

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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface, in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission pr

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32

Ajiev, Sergey S. "Singular and supersingular operators on function spaces, approximation and extrapolation." Phd thesis, 2004. http://hdl.handle.net/1885/148763.

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Lin, Ying-Chieh, and 林英杰. "Singular Integral Operators with Variable Kernels." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/43815040751882273795.

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博士<br>國立中央大學<br>數學研究所<br>96<br>The main purpose of this thesis is to investigate the weighted boundedness of the singular integral operators with variable kernels. First, we introduce the history of this theory. In Chapter 2, we recall the definitions of $A_p$ weights and the weighted Hardy spaces together with their properties. Next, we separate the smoothness of the variable kernel into two categories. The first is the class of kernels with smoothness in both variables. We adopt Kurtz-Wheeden''s method for our estimates to get the $L^p_w$ boundedness of the singular integral operators with

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Lee, Ming-Yi, and 李明憶. "Weighted Norm Inequalities of Singular Integral Operators." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/49818299622211741450.

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Tsai, Meng-che, and 蔡孟哲. "The weighted boundedness of singular integral operators." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/k823jw.

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碩士<br>國立中央大學<br>數學研究所<br>96<br>In this paper, we give some methods such that the operators are bounded from to . Under the condition related to the Muckenhoupt weights class, we realize that the proof of two weighted norm inequality only depends on one-weighted norm inequality. We give some examples to describe how did we prove it; that is, we proved that the maximal operator , the singular integral operator , the maximal singular integral operator , the Marcinkiewicz integral operator ,the Marcinkiewicz integral operator related to the area integral , and the Marcinkiewicz

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36

Shayya, Bassam Halim. "A class of strongly singular integral operators." 1996. http://catalog.hathitrust.org/api/volumes/oclc/35691507.html.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1996.<br>Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 45-46).

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Ibañez, Firnkorn Gonzalo Hugo. "Acotación de conmutadores de operadores integrales : dados por un núcleo a valores vectoriales que satisface una condición de tipo Hörmander y aplicaciones." Bachelor's thesis, 2015. http://hdl.handle.net/11086/2822.

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Se sabe que el todo conmutador de una integral singular esta acotado en normas Lp(w), con w un cierto peso, por un operador maximal apropiado. Para conmutadores de orden k de integrales singulares de Calderón-Zygmund (con núcleo satisfaciendo la condición de Lipschitz), el resultado clásico es: el operador que controla en normas p’s es el iterado k + 1 veces del operador maximal de Hardy-Littlewood. En este trabajo se definen condiciones que debe satisfacer un núcleo K de una integral singular a valores vectoriales para que su conmutador de orden k, es decir K ∈ H A,X,k, este acotado en norma

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George, A. J. "A Study On Solutions Of Singular Integral Equations." Thesis, 1995. https://etd.iisc.ac.in/handle/2005/1736.

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39

George, A. J. "A Study On Solutions Of Singular Integral Equations." Thesis, 1995. http://etd.iisc.ernet.in/handle/2005/1736.

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40

Lyall, Neil. "Strongly singular integral operators on the Heisenberg Group : L²-estimates /." 2004. http://www.library.wisc.edu/databases/connect/dissertations.html.

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Ibañez, Firnkorn Gonzalo Hugo. "Acotaciones de operadores integrales con condiciones de Hörmander generales." Doctoral thesis, 2020. http://hdl.handle.net/11086/16695.

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Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2020.<br>En esta tesis estudiamos acotaciones de tres tipos de operadores integrales fraccionarios y singulares con condiciones generales de tamaño y regularidad, utilizando técnicas modernas y clásicas. Primero consideramos operadores integrales fraccionarios que cumplan condiciones fraccionarias de tamaño y Lr-Hörmander, para los cuales probamos una dominación sparse adecuada y la acotación fuerte con pesos con control óptimo de la constante del peso. Luego consideramos o

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42

Ehrhardt, Torsten [Verfasser]. "Factorization theory for Toeplitz plus Hankel operators and singular integral operators with flip / von Torsten Ehrhardt." 2004. http://d-nb.info/972573305/34.

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Cho, Yong-Kum. "Multiparameter maximal operators and square functions on product spaces /." 1993. http://hdl.handle.net/1957/15879.

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Campos, Lina Isabel Fernandes. "Algumas classes de operadores integrais singulares com deslocamento e conjugação." Master's thesis, 2007. http://hdl.handle.net/10400.1/492.

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Schmäche, Christopher. "An obstacle problem for a fractional power of the Laplace operator." 2013. https://ul.qucosa.de/id/qucosa%3A16760.

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Abstract:

In dieser Arbeit setzen wir uns mit der Ph.D. Thesis von Luis Silvestre auseinander, in welcher er das Hindernisproblem für den gebrochenen Laplace Operator behandelt hat. Das Ziel war es seine Arbeit nachzuvollziehen und seine Beweise vollständig auszuformulieren. Dabei haben wir uns auf die Existenz der Lösung und erste Regularitätsresultate beschränkt.

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