Convergence of Eigenfunctions of a Steklov-Type Problem in a Half-Strip with a Small Hole

Abstract

We consider a Steklov-type problem for the Laplace operator in a half-strip containing a small hole with the Dirichlet conditions on the lateral boundaries and the boundary of the hole and the Steklov spectral condition on the base of the half-strip. We prove that eigenvalues of this problem vanish as the small parameter (the “diameter” of the hole) tends to zero.