Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains

We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M-0(+) (Omega)) for second order linear elliptic opera ors in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A(0), we prove that there exist a subsequence and a measure mu(0) in M-0(+)(D) such that the limit problem is the relaxed Dirichlet problem corresponding to A(0) and mu(0). We also prove a corrector result which provides an explicit approximation of the solutions in the H-1-norm, and which is obtained by. Multiplying the corrector for the H-converging matrices by some special test function which depends both on,the varying matrices and on the varying domains. (C) 2003 EIsevier SAS. All rights reserved.