Perturbation of the Laplacian spectrum when there is a change in the type of boundary condition on a small part of the boundary

Perturbations of Neumann's and Dirichlet's boundary-value problems for the Laplace operator in a bounded domain by changing to Dirichlet and Neumann boundary conditions, respectively, on a small part of the boundary are considered. For the perturbed boundary-value problems, the method of matched asymptotic expansions is used to construct the complete asymptotic forms of the smallest eigenvalues with respect to the small parameter characterizing the length of the small part of the boundary on which the type of boundary condition has been changed. (C) 1997 Elsevier Science Ltd.