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

TitleAsymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
Publication TypeJournal Article
Year of Publication2004
AuthorsDal Maso, G, Murat, F
JournalAnn. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486.
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.

URLhttp://hdl.handle.net/1963/1611

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