The third boundary value problem in potential theory for domains with a piecewise smooth boundary

Keywords

Mathematics, Neumann boundary condition, Domain (mathematical analysis), Boundary (topology), Boundary value problem

References

• Über lineare Funktionaltransformationen und FunktionalgleichungenJohann Radon — 1919
• Über das Neumann-Poincarésche problem für ein gebiet mit eckenTorsten Carleman — 1916
• Théorie des distributionsLaurent Schwartz — 1966
• Geometric Measure TheoryH. Fédérer — 1969
• Integral Operators in Potential TheoryJosef Král — 1980
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domainsGregory C. Verchota — 1984
• Corner singularity for transmission problems in three dimensionsStephan Rempel — 1989
• Eigenvalues for spherical domains with corners via boundary integral equationsStephan Rempel, G. Schmidt — 1991
• The Fredholm method in potential theoryJosef Král — 1966
• The double layer potential operator over polyhedral domains i: solvability in weighted sobolev spacesJohannes Elschner — 1992
• The Invertibility of the Double Layer Potential Operator in the Space of Continuous Functions Defined on a Polyhedron: The Panel MethodAndreas Rathsfeld — 1992
• The Dirichlet problem in non-smooth domainsDavid Jerison, Carlos E. Kenig — 1981
• On the convergence of Neumann series in Banach spaceNoboru Suzuki — 1976
• The Neumann problem on Lipschitz domainsDavid Jerison, Carlos E. Kenig — 1981
• A note on the Gauss-Green theoremHerbert Fédérer — 1958
• Su una teoria generale della misura (r − 1)-dimensionale in uno spazio adr dimensioniEnnio De Giorgi — 1954
• Boundary integral methods for the Laplace equationWilliam McLean — 1987
• The Gauss-Green theoremHerbert Fédérer — 1945
• On the convergence of Neumann series for noncompact operatorsDagmar Medková — 1991
• Leçons D'Analyse FonctionnelleLévy Paul — 1934

Cited by

• Solution of the Neumann problem for the Laplace equationDagmar Medková — 1998
• Solution of the Robin problem for the Laplace equationDagmar Medková — 1998
• Solution of the Dirichlet Problem for the Laplace equationDagmar Medková — 1999
• Neumann and Robin problems in a cracked domain with jump conditions on cracksDagmar Medková, П. А. Крутицкий — 2005
• The mixed harmonic problem in an exterior cracked domain with Dirichlet condition on cracksП. А. Крутицкий — 2005
• The Third Problem for the Laplace Equation with a Boundary Condition from LpDagmar Medková — 2006
• The Dirichlet–Neumann harmonic problem in a two–dimensional cracked domain with the Neumann condition on cracksП. А. Крутицкий — 2004
• The harmonic dirichlet problem for a cracked domain with jump conditions on cracksDagmar Medková, П. А. Крутицкий — 2004
• Boundedness of the solution of the third problem for the Laplace equationDagmar Medková — 2005
• Single and Double Layer Potentials on Domains with Conical Points I: Straight ConesYu Qiao, Victor Nistor — 2012
• Which solutions of the third problem for the Poisson equation are boundedDagmar Medková — 2004
• The mixed harmonic problem in a bounded cracked domain with Dirichlet condition on cracksП. А. Крутицкий — 2004
• Continuous Extendibility of Solutions of the Third Problem for the Laplace EquationDagmar Medková — 2003
• The Robin problem for the scalar Oseen equationDagmar Medková, Emma Skopin, Werner Varnhorn — 2013
• The integral representation for a solution of the 2-d Dirichlet problem with boundary data on closed and open curvesП. А. Крутицкий — 2000
• The Oblique Derivative Problem for the Laplace Equation in a Plain DomainDagmar Medkov� — 2004
• Boundary value problems for the laplace equation using integral equation approachGazi Özdemir — 2016
• Point Electrode Problems in Piecewise Smooth Plane DomainsOtto Seiskari — 2012
• Double Layer Potentials on Polygons and Pseudodifferential Operators on Lie GroupoidsYu Qiao, Hengguang Li — 2018
• Infinitely Many Embedded Eigenvalues for the Neumann-Poincaré Operator in 3DWei Li, Karl‐Mikael Perfekt, Stephen P. Shipman — 2020

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