A regularity theory for random elliptic operators

Abstract : The qualitative theory of stochastic homogenization of uniformly elliptic linear (but possibly non-symmetric) systems in divergence form is well-understood. Quantitative results on the speed of convergence, and on the error in the representative volume method, like those recently obtained by the authors for scalar equations, require a type of stochastic regularity theory for the corrector (e.g., higher moment bounds). One of the main insights of the very recent work of Armstrong and Smart is that one should separate these error estimates, which require strong mixing conditions in order to yield optimal rates, from the (large scale) regularity theory for a-harmonic functions, which by the philosophy of Avellaneda and Lin from periodic homogenization are expected to hold under weak mixing conditions. In this paper, we establish the regularity theory for non-symmetric systems under a mild mixing condition.
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https://hal.archives-ouvertes.fr/hal-01093368
Contributor : Antoine Gloria <>
Submitted on : Wednesday, December 10, 2014 - 3:35:27 PM
Last modification on : Monday, August 20, 2018 - 9:44:02 AM

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  • HAL Id : hal-01093368, version 1
  • ARXIV : 1409.2678

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Antoine Gloria, Stefan Neukamm, Felix Otto. A regularity theory for random elliptic operators . 2014. ⟨hal-01093368⟩

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