%0 Journal Article
%T Concentrated terms and varying domains in elliptic equations: Lipschitz case
%A G. S. Arag£żo
%A S. M Bruschi
%J Mathematics
%D 2014
%I arXiv
%X In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior which is uniformly Lipschitz and nonlinear terms are concentrated in a region which neighbors the boundary domain. We prove that this family of solutions converges to the solutions of a limit problem in H^1 , an elliptic equation with nonlinear boundary conditions which captures the oscillatory behavior of the boundary and whose nonlinear terms are transformed into a flux condition on the boundary. Indeed, we show the upper semicontinuity of this family of solutions.
%U http://arxiv.org/abs/1412.5850v1