Stability of the Neumann problem for variations of the boundary

Authors
Bucur, D Varchon, N
Citation
D. Bucur et N. Varchon, Stability of the Neumann problem for variations of the boundary, CR AC S I, 331(5), 2000, pp. 371-374
Citations number
12
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
331
Issue
5
Year of publication
2000
Pages
371 - 374
Database
ISI
SICI code
0764-4442(20000901)331:5<371:SOTNPF>2.0.ZU;2-I
Abstract
We give a stability result for the solution of a two-dimensional elliptic p roblem with Neumann boundary conditions with respect to the geometric domai n variation. The perturbations are given in the Hausdorff topology and the stability holds if two conditions are satisfied: the number of the connecte d components of the complement of the variable domain is uniformly bounded and the Lebesgue measure is stable. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.