Corner singularity for transmission problems in three dimensions

DOI10.1007/BF01196880zbMath0695.47046MaRDI QIDQ909982

Stephan Rempel

Publication date: 1989

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

Sobolev spacesunique solvabilitybehaviour of the solution near the cornermeromorphic family of one-dimensional integral operators on a geodesic polygon on the two spheretransmission problem for the Laplace operator

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) General theory of partial differential operators (47F05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items

The double layer potential operator over polyhedral domains i: solvability in weighted sobolev spaces, The Invertibility of the Double Layer Potential Operator in the Space of Continuous Functions Defined on a Polyhedron: The Panel Method, Variable coefficient transmission problems and singular integral operators on non-smooth manifolds, Transmission boundary problems for Dirac operators on Lipschitz domains and applications to Maxwell’s and Helmholtz’s equations, The third boundary value problem in potential theory for domains with a piecewise smooth boundary, Eigenvalues for spherical domains with corners via boundary integral equations

Cites Work

• A direct boundary integral equation method for transmission problems
• Singularities of the solution to the Dirichlet problem for a second-order equation in a neighborhood of an edge
• Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain
• Eigenvalues of the Laplacian in Two Dimensions
• A deconvolution problem with the kernel 1/[x on the plane]
• Edge Behavior of the Solution of an Elliptic Problem
• Transmission problems for the Helmholtz equation
• Decompositions in Edge and Corner Singularities for the Solution of the Dirichlet Problem of the Laplacian in a Polyhedron
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