A mixed problem for the Laplace operator in a domain with moderately close holes

DOI10.1080/03605302.2015.1135166zbMath1353.35144arXiv1903.05856OpenAlexW2313367116MaRDI QIDQ3188118

Matteo Dalla Riva, Paolo Musolino

Publication date: 16 August 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.05856

zbMATH Keywords

asymptotic expansionLaplace operatormixed problemmoderately close holes

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) PDEs of mixed type (35M10) Asymptotic expansions of solutions to PDEs (35C20) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Linear integral equations (45A05)

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The Dirichlet problem in a planar domain with two moderately close holes ⋮ A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary ⋮ Converging expansions for Lipschitz self-similar perforations of a plane sector ⋮ A nonlinear problem for the Laplace equation with a degenerating Robin condition ⋮ The functional analytic approach for quasi-periodic boundary value problems for the Helmholtz equation ⋮ Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary

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