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Continuity with respect to the domain in the Neumann problem. (Continuité par rapport au domaine dans le problème de Neumann.) (French) Zbl 0805.35010
Summary: It is proved the continuity of the solution of the Neumann problem for the Laplacian in terms of its integration domain, if this presents cracks and satisfies some capacitary constraints. On the space of domains it is considered the Hausdorff complementary topology in which the family of constrained domains is compact.

35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations