A stability result for nonlinear Neumann problems in Reifenberg flat domains in Rn

• Autores: Antoine Lemenant, Emmanouil Milakis
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 55, Nº 2, 2011, págs. 413-432
• Idioma: inglés
• DOI: 10.5565/publmat_55211_08
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• Resumen

  • In this paper we prove that if k is a sequence of Reifenberg-flat domains in RN that converges to for the complementary Haus- dorff distance and if in addition the sequence k has a �uniform size of holes�, then the solutions uk of a Neumann problem of the form (0.1) ( -div a(x,ruk) + b(x, uk) = 0 in k a(x,ruk) ·  = 0 on @ k converge to the solution u of the same Neumann problem in .

    The result is obtained by proving the Mosco convergence of some Sobolev spaces, that follows from the extension property of Reifenberg-flat domains.