Preprint 81/2015

The Corrector in Stochastic Homogenization: Near-Optimal Rates With Optimal Stochastic Integrability

Antoine Gloria and Felix Otto

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Submission date: 24. Nov. 2015
Pages: 71
MSC-Numbers: 35J15, 35K10, 35B27, 60H25, 60F99
Keywords and phrases: stochastic homogenization, corrector, quantitative estimate
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Abstract:
We consider uniformly elliptic coefficient fields that are randomly distributed according to a stationary ensemble of a finite range of dependence. We show that the gradient ϕ of the corrector ϕ, when spatially averaged over a scale R 1 decays like Rα for any α<d 2. We establish these rates on the level of Gaussian bounds in terms of the stochastic integrability.

03.04.2017, 12:08