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Dirichlet problems on varying domains. (English) Zbl 1090.35069
Summary: The aim of the paper is to characterise sequences of domains for which solutions to an elliptic equation with Dirichlet boundary conditions converge to a solution of the corresponding problem on a limit domain. Necessary and sufficient conditions are discussed for strong and uniform convergence for the corresponding resolvent operators. Examples are given to illustrate that most results are optimal.

MSC:
35J25 Boundary value problems for second-order elliptic equations
35B25 Singular perturbations in context of PDEs
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