Uniform Asymptotics of Green's Kernels for Mixed and Neumann Problems in Domains with Small Holes and Inclusions

DOI10.1007/978-0-387-85652-0_6zbMath1171.35027OpenAlexW1861267831MaRDI QIDQ3613596

Vladimir Gilelevich Maz'ya, Alexander B. Movchan

Publication date: 12 March 2009

Published in: Sobolev Spaces in Mathematics III (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-387-85652-0_6

zbMATH Keywords

singularly perturbed domainsAsymptotic formulas for Green kernels

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Asymptotic expansions of solutions to PDEs (35C20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cites Work

• Uniform asymptotic formulae for Green's functions in singularly perturbed domains
• Uniform asymptotic formulae for Green's kernels in regularly and singularly perturbed domains
• Estimates in 𝐿_{𝑝} and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
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