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Stochastic diffeomorphisms and homogenization of multiple integrals

Antoine Gloria 1
1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : In a recent work, Blanc, Le Bris and Lions have introduced the notion of stochastic diffeomorphism together with a variant of stochastic homogenization theory for linear and monotone elliptic operators. Their proofs rely on the ergodic theorem and on the analysis of the associated corrector equation. In the present article, we provide another proof of their results using the formalism of integral functionals. We also extend the analysis to cover the case of quasiconvex integrands.
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Submitted on : Friday, October 5, 2007 - 10:04:06 AM
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Antoine Gloria. Stochastic diffeomorphisms and homogenization of multiple integrals. Applied Mathematics Research eXpress, Oxford University Press (OUP): Policy H - Oxford Open Option A, 2008, 2008 (abn001), pp.1-23. ⟨10.1093/amrx/abn001⟩. ⟨inria-00176568v2⟩

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