| Abstract: |
| I will present some regularity estimates related to the stochastic homogenization for nondivergence form elliptic 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. This is a necessary ingredient in obtaining optimal error estimates for the stochastic homogenization of linear uniformly elliptic equations. |
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