A singularly perturbed mixed boundary value problem

Martin Costabel and Monique Dauge

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 parameter ε and tends to a Dirichlet condition as ε --> 0. We give a complete asymptotic expansion of the solution in powers of ε . 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 O( ε log ε ).

Published in Comm. Partial Differential Equations 21 (11-12), 1996, 1919--1949.

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