On the eigenvalues and eigenfunctions of the Dirichlet and Neumann problems in a domain with perforated partitions

DOI10.1134/S0012266121060045zbMath1469.35162OpenAlexW3177535655MaRDI QIDQ2042590

Sergueï A. Nazarov

Publication date: 21 July 2021

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

Full work available at URL: https://doi.org/10.1134/s0012266121060045

zbMATH Keywords

singularly perturbed domainsholes of small diameterssplitting of multiple eigenvalues of the limit problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

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Localization of eigenfunctions in the Dirichlet beaker

Cites Work

• Singularities of solutions of the Neumann problem at a conical point
• Elliptic problems in domains with piecewise smooth boundaries
• Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary condition
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• ASYMPTOTIC EXPANSIONS OF THE EIGENVALUES OF BOUNDARY VALUE PROBLEMS FOR THE LAPLACE OPERATOR IN DOMAINS WITH SMALL HOLES
• [Russian Text Ignored.]
• The polynomial property of self-adjoint elliptic boundary-value problems and an algebraic description of their attributes
• Mode matching methods for spectral and scattering problems
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