On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary

DOI10.1007/s13163-017-0243-4zbMath1382.35025OpenAlexW2752791989MaRDI QIDQ1695719

M. Eugenia Pérez, Sergueï A. Nazarov

Publication date: 8 February 2018

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10902/11828

zbMATH Keywords

corner singularitiesmixed boundary-value problemSteklov problemtwo-term asymptoticsasymptotic forms of eigenfunctionsasymptotic splitting of eigenvalues

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) General topics in linear spectral theory for PDEs (35P05) Vibrations in dynamical problems in solid mechanics (74H45) Eigenvalue problems for linear operators (47A75) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (9)

Membranes with thin and heavy inclusions: Asymptotics of spectra ⋮ Homogenization of Winkler-Steklov spectral conditions in three-dimensional linear elasticity ⋮ Pointwise fixation along the edge of a Kirchhoff plate ⋮ Localization effects for Dirichlet problems in domains surrounded by thin stiff and heavy bands ⋮ Spectral singularities of solutions to a boundary-value problem for the Fredholm integro-differential equation of the second order with reflection of argument ⋮ Asymptotic structure of the spectrum in a Dirichlet-strip with double periodic perforations ⋮ On the behavior of the spectrum of a perturbed Steklov boundary value problem with a weak singularity ⋮ Asymptotic expansions for the conductivity problem with nearly touching inclusions with corner ⋮ Homogenization of Kirchhoff plates joined by rivets which are modeled by the Sobolev point conditions

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