On a singularly perturbed Steklov problem in a domain perforated along the boundary

Abstract We study the asymptotic behavior of solutions and eigenelements to a boundary value problem for the Laplace equation in a domain perforated along part of the boundary. On the boundary of holes, we set the homogeneous Dirichlet boundary condition and the Steklov spectral condition on the mentioned part of the outer boundary of the domain. Assuming that the boundary microstructure is periodic, we construct the limit problem and prove the homogenization theorem