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Continuity with respect to the domain for the Laplacian: A survey. (English) Zbl 0822.35029

Summary: We present several results of continuity with respect to the domain for the solution of problems with the Laplacian. We consider the usual homogeneous Dirichlet problem, then the Poisson problem and, at last, the Neumann problem. Some different kinds of convergence of the domains are taken in account and we always assume the minimum of regularity for the domains.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35B35 Stability in context of PDEs
35B20 Perturbations in context of PDEs
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