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

Abstract

In this paper we prove that if ωk is a sequence of Reifenberg-flat domains in RN that converges to ω for the complementary Haus- dorff distance and if in addition the sequence ωk has a "uniform size of holes", then the solutions uk of a Neumann problem of the form (0.1) ( -div a(x,▽uk) + b(x, uk) = 0 in ωk a(x,▽uk) · v = 0 on ∂ωk converge to the solution u of the same Neumann problem in ω. The result is obtained by proving the Mosco convergence of some Sobolev spaces, that follows from the extension property of Reifenberg-flat domains.