A SINGULARLY PERTURBED MIXED BOUNDARY-VALUE PROBLEM

We study a mixed Neumann-Robin boundary value problem for the Laplace operator in a smooth domain in R(2). The Robin condition contains a pa rameter epsilon and tends to a Dirichlet condition as epsilon --> 0. W e give a complete asymptotic expansion of the solution in powers of ep silon. At the points where the boundary conditions change, there appea r boundary layers of corner type of size epsilon. They describe how th e singularities of the limit Dirichlet-Neumann problem are approximate d. We give sharp estimates in various Sobolev norms and show in partic ular that there exist terms of order O (epsilon log epsilon).