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 (Ω)) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H -converge to a matrix A , we prove that there exist a subsequence and a measure μ in M 0 (Ω) such that the limit problem is the relaxed Dirichlet problem corresponding to A and μ . We also prove a corrector result which provides an explicit approximation of the solutions in the H -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.