Homogenization of a nonlinear elliptic problem with large nonlinear potential

Abstract

Homogenization is studied for a nonlinear elliptic boundary-value problem with a large nonlinear potential. More specifically we are interested in the asymptotic behaviour of a sequence of p-Laplacians of the form It is shown that, under a centring condition on the potential V, there exists a two-scale homogenized system with solution (u, u 1) such that the sequence u ϵ of solutions converges weakly to u in W 1,p and the gradients D x u ϵ two-scale converges weakly to D x u + D y u 1 in L p , respectively. We characterize the limit system explicitly by means of two-scale convergence and a new convergence result.