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Boundary variation for a Neumann problem. (English) Zbl 1072.35063
The authors study the stability of the solution of a two-dimensional elliptic problem with Neumann boundary conditions for geometric domain perturbations in the Hausdorff topology. The stability result is obtained assuming that the number of the connected components of the complement of the variable domain is uniformly bounded and the Lebesgue measure is stable.

MSC:
35J20 Variational methods for second-order elliptic equations
35B20 Perturbations in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
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