Lipschitz Regularity for Elliptic Equations with Random Coefficients
Armstrong, Scott N.; Mourrat, Jean-Christophe (2016), Lipschitz Regularity for Elliptic Equations with Random Coefficients, Archive for Rational Mechanics and Analysis, 219, 1, p. 255-348. 10.1007/s00205-015-0908-4
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1411.3668v3
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)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 (for example finite range of dependence). We also prove a quenched L2 estimate for the error in homogenization of Dirichlet problems. The approach is based on subadditive arguments which rely on a variational formulation of general quasilinear divergence-form equations.
Subjects / Keywordsquasilinear elliptic equations
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