@article {2004,
title = {Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains},
journal = {Ann. Inst. H. Poincar{\'e}. Anal. Non Lin{\'e}aire 21 (2004), (4), p. 445-486.},
number = {SISSA;40/2002/M},
year = {2004},
publisher = {SISSA Library},
abstract = {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.},
url = {http://hdl.handle.net/1963/1611},
author = {Gianni Dal Maso and Francois Murat}
}