Lipschitz Regularity for Elliptic Equations with Random Coefficients

Abstract : We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale L ∞-type estimate for the gradient of a solution. The estimate is proved with optimal stochastic integrability under a one-parameter family of mixing assumptions, allowing for very weak mixing with non-integrable correlations to very strong mixing (e.g., finite range of dependence). We also prove a quenched L 2 estimate for the error in ho-mogenization of Dirichlet problems. The approach is based on subadditive arguments which rely on a variational formulation of general quasilinear divergence-form equations.
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Submitted on : Wednesday, November 23, 2016 - 10:34:50 PM
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Scott Armstrong, Jean-Christophe Mourrat. Lipschitz Regularity for Elliptic Equations with Random Coefficients. Archive for Rational Mechanics and Analysis, Springer Verlag, 2016, 219, pp.255 - 348. ⟨10.1007/s00205-015-0908-4⟩. ⟨ensl-01401892⟩

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