Eigenvalues of the Laplacian with moving mixed boundary conditions: the case of disappearing Dirichlet region (Q2225893)

The paper is devoted to the eigenvalue problem for the Laplacian on a bounded Lipschitz domain and a singular perturbation of it, with mixed Dirichlet-Neumann homogeneous boundary conditions. The authors study the behaviour of a perturbed eigenvalue when the region where Dirichlet boundary conditions are prescribed is disappearing in some suitable sense.