Singular perturbations of curved boundaries in three dimensions. The spectrum of the Neumann Laplacian

DOI10.4171/ZAA/1429zbMath1228.35022OpenAlexW1983589575MaRDI QIDQ537679

Antoine Laurain, Jan Sokolowski, Sergueï A. Nazarov

Publication date: 20 May 2011

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1429

zbMATH Keywords

asymptotic of eigenvalues and eigenfunctionsperturbation of domain

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Estimates of eigenvalues in context of PDEs (35P15) Eigenvalue problems for linear operators (47A75) Asymptotic expansions of solutions to PDEs (35C20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Perturbations in context of PDEs (35B20)

Related Items (6)

Hadamard type asymptotics for eigenvalues of the Neumann problem for elliptic operators ⋮ Topological derivatives of shape functionals. I: Theory in singularly perturbed geometrical domains ⋮ Asymptotics of solutions to the spectral elasticity problem for a two-dimensional body with a small cavern ⋮ Ramification of multiple eigenvalues for the Dirichlet-Laplacian in perforated domains ⋮ Asymptotic expansions for eigenvalues of the Steklov problem in singularly perturbed domains ⋮ Topological Derivative for PDEs on Surfaces

Cites Work

• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• The method of matched asymptotic expansions in the problem of the Helmholtz acoustic resonator
• Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary condition
• Asymptotics of the solution of the Dirichlet problem in domains with a thin crosspiece
• Variational methods in shape optimization problems
• ASYMPTOTIC EXPANSIONS OF THE EIGENVALUES OF BOUNDARY VALUE PROBLEMS FOR THE LAPLACE OPERATOR IN DOMAINS WITH SMALL HOLES
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