TY - JOUR T1 - Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains JF - Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. Y1 - 2004 A1 - Gianni Dal Maso A1 - Francois Murat AB - We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators 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 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1611 U1 - 2507 U2 - Mathematics U3 - Functional Analysis and Applications ER -