A Singularly mixed boundary value problem

We study a mixed Neumann-Robin boundary value problem for the Laplace operator in a smooth domain in R2The Robin condition contains a parameter e and tends to a Dirichlet condition as . We give a complete asymptotic expansion of the solution in powers of e. At the points where the boundary conditions change, there appear boundary layers of corner type of size ϵ. They describe how the singularities of the limit Dirichlet-Neumann problem are approximated. We give sharp estimates in various Sobolev norms and show in particular that there exist terms of order