On a problem with nonperiodic frequent alternation of boundary condition imposed on fast oscillating sets

Abstract

We consider singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent and nonperiodic alternation of boundary conditions imposed on narrow strips lying in the lateral surface. The width of strips depends on a small parameter in a arbitrary way and may oscillate fast, moreover, the nature of oscillation is arbitrary, too. We obtain two-sided estimates for degree of convergences of the perturbed eigenvalues.