Transmission problem for the Laplace equation and the integral equation method

DOI10.1016/j.jmaa.2011.09.041zbMath1233.35076OpenAlexW2092453899MaRDI QIDQ655487

Dagmar Medková

Publication date: 4 January 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.09.041

zbMATH Keywords

boundary integral equationLaplace equationdouble layer potentialsuccessive approximationtransmission problemsingle layer potential

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral operators (45P05) Weak solutions to PDEs (35D30)

Related Items (10)

Neumann-transmission problems for pseudodifferential Brinkman operators on Lipschitz domains in compact Riemannian manifolds ⋮ A local regularization scheme of Cauchy problem for the Laplace equation on a doubly connected domain ⋮ Ground-state solutions to a Kirchhoff-type transmission problem ⋮ Layer potential analysis for a Dirichlet‐transmission problem in Lipschitz domains in ℝⁿ ⋮ Representations of solutions of Laplacian boundary value problems on exterior regions ⋮ Normalized solutions for an horizontal transmission problem ⋮ Ground-state solutions to Kirchhoff-type transmission problems with critical perturbation ⋮ Interface boundary value problems of Robin-transmission type for the Stokes and Brinkman systems on n -dimensional Lipschitz domains: applications ⋮ Dirichlet-transmission problems for pseudodifferential Brinkman operators on Sobolev and Besov spaces associated to Lipschitz domains in Riemannian manifolds ⋮ Infinitely many positive harmonic functions with an oscillating boundary condition on exterior regions

Cites Work

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• The Poisson's problem for the Laplacian with Robin boundary condition in non-smooth domains
• An introduction to Sobolev spaces and interpolation spaces
• The integral equation method and the Neumann problem for the Poisson equation on NTA domains
• The method of layer potentials for non-smooth domains with arbitrary topology
• Transmission problems and spectral theory for singular integral operators on Lipschitz domains
• Brinkman-type operators on Riemannian manifolds: Transmission problems in Lipschitz and \(C ^{1}\) domains
• Potential techniques and regularity of boundary value problems in exterior non-smooth domains
• Les potentiels d'energie finie
• Boundary integral equations for a three-dimensional Brinkman flow problem
• The Neumann problem for the Laplace equation on general domains
• On a Regularity Theorem for Weak Solutions to Transmission Problems with Internal Lipschitz Boundaries

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