Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary

DOI10.1080/03605302.2020.1840585zbMath1460.35078OpenAlexW3112993413MaRDI QIDQ4965954

Marc Dambrine, Matteo Dalla Riva, Paolo Musolino, Virginie Bonnaillie-Noël

Publication date: 18 March 2021

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

Full work available at URL: https://doi.org/10.1080/03605302.2020.1840585

zbMATH Keywords

Dirichlet problemLaplace operatorsingularly perturbed perforated domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cites Work

• Asymptotic behaviour of the conformal representation of a Jordan domain with a small hole in Schauder spaces
• Asymptotic theory of elliptic boundary value problems in singularly perturbed domains. Vol. II. Transl. from the German by Boris Plamenevskii
• 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
• Green's kernels and meso-scale approximations in perforated domains
• A mixed problem for the Laplace operator in a domain with moderately close holes
• INTERACTIONS BETWEEN MODERATELY CLOSE INCLUSIONS FOR THE LAPLACE EQUATION
• Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface
• Series expansions for the solution of the Dirichlet problem in a planar domain with a small hole
• Asymptotic behavior of the solutions of the Dirichlet problem for the Laplace operator in a domain with a small hole. A functional analytic approach
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