Spectral Problem with Steklov Condition
on a Thin Perforated Interface

R. R. Gadyl’shin^{a, b}, A. L. Piatnitski^{c, d}, and G. A. Chechkin^e

Presented by Academician of the RAS V.V. Kozlov August 26, 2015

Received September 10, 2015

Abstract—A two-dimensional Steklov-type spectral problem for the Laplacian in a domain divided into two
parts by a perforated interface with a periodic microstructure is considered. The Steklov boundary condition is
set on the lateral sides of the channels, a Neumann condition is specified on the rest of the interface, and a
Dirichlet and Neumann condition is set on the outer boundary of the domain. Two-term asymptotic expansions
of the eigenvalues and the corresponding eigenfunctions of this spectral problem are constructed.

DOI: 10.1134/S1064562416010191

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