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Zbl 1072.35063
Bucor, Dorin; Varchon, Nicolas
Boundary variation for a Neumann problem. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29, No. 4, 807-821 (2000). ISSN 0391-173X

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.
[Leszek Gasiński (Kraków)]
MSC 2000:
*35J20 Second order elliptic equations, variational methods
35B20 Perturbations (PDE)
35J25 Second order elliptic equations, boundary value problems

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