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Pré-Publication, Document De Travail Année : 2007

Stochastic homogenization and random lattices

Résumé

We present some variants of stochastic homogenization theory for scalar elliptic equations of the form -div[ A(x/ε,ω) ∇ u] = f. These variants basically consist in defining stochastic coefficients A(x/ε,ω) from stochastic deformations (using random diffeormorphisms) of the periodic setting, as announced in [4]. The settings we define are not covered by the existing theories. We also clarify the relation between this type of questions and our construction, performed in [3,5], of the energy of, both deterministic and stochastic, microscopic infinite sets of points in interaction.
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Dates et versions

hal-00140076 , version 1 (04-04-2007)

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  • HAL Id : hal-00140076 , version 1

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Xavier Blanc, Claude Le Bris, Pierre Louis Lions. Stochastic homogenization and random lattices. 2007. ⟨hal-00140076⟩
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