Lipschitz Regularity for Elliptic Equations with Random Coefficients

Scott N. Armstrong, Jean Christophe Mourrat

Research output: Contribution to journalArticle

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 (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.

Original languageEnglish (US)
Pages (from-to)255-348
Number of pages94
JournalArchive for Rational Mechanics and Analysis
Volume219
Issue number1
DOIs
StatePublished - Jan 1 2016

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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