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Large-scale regularity in stochastic homogenization with divergence-free drift (2006.16892v2)

Published 30 Jun 2020 in math.PR and math.AP

Abstract: We provide a simple proof of quenched stochastic homogenization for random environments with a mean zero, divergence-free drift under the assumption that the drift admits a stationary $Ld$-integrable stream matrix in $d\geq 3$ or an $L{2+\delta}$-integrable stream matrix in $d=2$. In addition, we prove that the environment almost surely satisfies a large-scale H\"older regularity estimate and first-order Liouville principle.

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