Asymptotic expansion of eigenelements of the Laplace operator in a domain with a large number of ‘light’ concentrated masses sparsely situated on the boundary. Two-dimensional case

DOI10.1090/S0077-1554-09-00177-0zbMath1202.35143OpenAlexW2028160447MaRDI QIDQ3057479

Gregory A. Chechkin

Publication date: 24 November 2010

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0077-1554-09-00177-0

zbMATH Keywords

singular perturbationsLaplace operatorasymptotic expansionseigenoscillations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Membranes (74K15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (4)

On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary ⋮ Perturbation by slender potential of operators associated with sectorial forms ⋮ Estimate of the spectrum deviation of the singularly perturbed Steklov problem ⋮ Spatial-skin effect for eigenvibrations of a thick cascade junction with ‘heavy’ concentrated masses

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