On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type

DOI10.1070/IM8674zbMath1406.35032OpenAlexW2810913221MaRDI QIDQ4613518

Andrey L. Piatnitski, Gregory A. Chechkin, Rustem R. Gadyl'shin

Publication date: 1 February 2019

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im8674

zbMATH Keywords

periodic microstructureSteklov problemtwo-term asymptotic formulahomogenization of spectral problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Asymptotic expansions of solutions to PDEs (35C20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (6)

Effective transmission conditions for reaction–diffusion processes in domains separated by thin channels ⋮ Operator estimates for elliptic problem with rapidly alternating Steklov boundary condition ⋮ On elliptic operators with Steklov condition perturbed by Dirichlet condition on a small part of boundary ⋮ Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition ⋮ On the behavior of the spectrum of a perturbed Steklov boundary value problem with a weak singularity ⋮ Singular Limit for Reactive Diffusive Transport Through an Array of Thin Channels in case of Critical Diffusivity

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