Homogenization and asymptotics for a membrane with closely spaced clamping points (Q1395158)

A two-dimensional boundary value problem with a frequently varying type of boundary conditions is considered for the Laplace operator. Conditions are presented under which the limit boundary value problem is a Neumann or a mixed problem. The first few terms of the asymptotic representations of the eigenvalues and the corresponding eigenfunctions are constructed in the case of the Neumann limit problem.