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
MSC-Numbers: 35J15, 35K10, 35B27, 60H25, 60F99
Keywords and phrases: stochastic homogenization, corrector, quantitative estimate
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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 R−α for any α<. We establish these rates on the level of Gaussian bounds in terms of the stochastic integrability.