A singularly perturbed mixed boundary value problem
Martin Costabel, Monique Dauge · Communications in Partial Differential Equations · 1996
We study a mixed Neumann-Robin boundary value problem of the Laplace operator in a smooth domain in R{sup 2}. The Robin condition contains a parameter {var_epsilon} and tends to a Dirichlet condition as {var_epsilon} {yields} 0. We give a complete asymptotic expansion of the solution in powers of {var_epsilon}. At the points where the boundary conditions change, there appear boundary layers of corner type of size {var_epsilon}. 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 O ({var_epsilon} log {var_epsilon}). 12 refs.