Spectral Problem with Steklov Condition on a Thin Perforated Interface

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.