Mixed problem for the Laplace equation outside cuts in a plane with setting Dirichlet and skew derivative conditions on different sides of the cuts

DOI10.1090/S0033-569X-06-00987-0zbMath1143.35020OpenAlexW2082161569MaRDI QIDQ3429100

A. I. Sgibnev, P. A. Krutitskii

Publication date: 30 March 2007

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0033-569x-06-00987-0

zbMATH Keywords

singularitiesintegral representationLaplace equationmixed problemasymptotic formulascuts

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) Fredholm integral equations (45B05)

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Problem for the diffusion equation outside cuts on the plane with the Dirichlet condition and an oblique derivative condition on opposite sides of the cuts ⋮ A problem for the Helmholtz equation outside cuts on the plane with the Dirichlet condition and the oblique derivative condition on opposite sides of the cuts

Cites Work

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• The method of integral equations in the mixed Dirichlet-Neumann problem for the Laplace equation in the exterior of cuts in the plane
• THE ANGULAR POTENTIAL AND SOME OF ITS APPLICATIONS
• On the electric current from electrodes in a magnetized semiconductor film