A singularly perturbed mixed boundary value problem
Journal Article
·
· Communications in Partial Differential Equations
OSTI ID:530804
- Universite de Rennes (France)
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.
- OSTI ID:
- 530804
- Journal Information:
- Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 11-12 Vol. 21; ISSN 0360-5302; ISSN CPDIDZ
- Country of Publication:
- United States
- Language:
- English
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