Representation of a solution of the Dirichlet problem in a planar cusp domain as a logarithmic single-layer potential

DOI10.3103/S1063454110030088zbMath1262.35084OpenAlexW2077019660MaRDI QIDQ1759477

S. V. Poborchii

Publication date: 21 November 2012

Published in: Vestnik St. Petersburg University. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1063454110030088

zbMATH Keywords

Dirichlet problemboundary integral equationLaplace equationlogarithmic potential

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) Linear integral equations (45A05)

Cites Work

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• Unique solvability of the integral equation for harmonic simple layer potential on the boundary of a domain with a peak
• On representation of the solution of the Neumann problem in a domain with peak by the harmonic simple layer potential

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