Homogenization of the Dirichlet problem for a system of quasilinear elliptic equations in a domain with fine-grained boundary

We study the Dirichlet problem for a system of nonlinear elliptic equations of Leray-Lions type in a sequence of domains Omega((s)), s = 1, 2,..., with fine-grained boundaries. Under appropriate structure conditions on the system and the geometry of Omega((s)), we prove that the sequence of solutions of the problem converges in suitable topologies to the solution of a limit problem which contains an additional term of capacity type.We construct the limit problem. 2003 Editions scientifiques et medicales Elsevier SAS.