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Title:听听Regularity Estimates for the Stochastic Homogenization of Elliptic Nondivergence Form Equations
Abstract:听I will present some regularity estimates related to the stochastic homogenization for nondivergence form equations. In a joint work with Scott Armstrong, we show that in the stochastic homogenization for linear uniformly elliptic equations in random media, solutions actually exhibit improved regularity properties in light of the homogenization process. In particular, we show that with extremely high probability, solutions of the random equation have almost the same regularity as solutions of the deterministic homogenized equation. The argument is similar to the proof of the classical Schauder estimates, however it utilizes the random structure of the problem to obtain improvement.听

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