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Article Dans Une Revue Journal of the European Mathematical Society Année : 2017

Quantitative results on the corrector equation in stochastic homogenization

Résumé

We derive optimal estimates in stochastic homogenization of linear elliptic equations in divergence form in dimensions $d\ge 2$. In previous works we studied the model problem of a discrete elliptic equation on $\mathbb{Z}^d$. Under the assumption that a spectral gap estimate holds in probability, we proved that there exists a stationary corrector field in dimensions $d>2$ and that the energy density of that corrector behaves as if it had finite range of correlation in terms of the variance of spatial averages - the latter decays at the rate of the central limit theorem. In this article we extend these results, and several other estimates, to the case of a continuum linear elliptic equation whose (not necessarily symmetric) coefficient field satisfies a continuum version of the spectral gap estimate. In particular, our results cover the example of Poisson random inclusions.

Dates et versions

hal-01093381 , version 1 (10-12-2014)

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Citer

Antoine Gloria, Felix Otto. Quantitative results on the corrector equation in stochastic homogenization. Journal of the European Mathematical Society, 2017, 19 (11), pp.3489-3548. ⟨10.4171/JEMS/745⟩. ⟨hal-01093381⟩
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