Dirichlet problem for the Laplace equation in the exterior of open Lipschitz surfaces

DOI10.1134/S1064562412030222zbMath1262.35092OpenAlexW1995677343MaRDI QIDQ1761027

P. A. Krutitskii

Publication date: 15 November 2012

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562412030222

zbMATH Keywords

existenceuniquenessintegral representationopen Lipschitz surfaces

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Cites Work

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• On the properties of solutions of the harmonic Dirichlet problem in a two-dimensional domain with cuts
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• The 2-dimensional Dirichlet problem in an external domain with cuts
• On existence of a classical solution and non-existence of a weak solution to the Dirichlet problem in a planar domain with slits for Laplacian
• The Neumann problem on Lipschitz domains
• The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts
• On finding the asymptotes to the solutions of short-wate diffraction problems

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