Lipschitz Regularity for Elliptic Equations with Random Coefficients

Scott 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

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Random Coefficients
Elliptic Equations
Lipschitz
Regularity
Divergence
Estimate
Weak Mixing
Quasilinear Elliptic Systems
Regularity Theory
Strong Mixing
Quasilinear Elliptic Equation
Variational Formulation
Homogenization
Dirichlet Problem
Integrability
Gradient
Range of data
Form

ASJC Scopus subject areas

  • Analysis
  • Mechanical Engineering
  • Mathematics (miscellaneous)

Cite this

Lipschitz Regularity for Elliptic Equations with Random Coefficients. / Armstrong, Scott; Mourrat, Jean Christophe.

In: Archive for Rational Mechanics and Analysis, Vol. 219, No. 1, 01.01.2016, p. 255-348.

Research output: Contribution to journalArticle

Armstrong, Scott ; Mourrat, Jean Christophe. / Lipschitz Regularity for Elliptic Equations with Random Coefficients. In: Archive for Rational Mechanics and Analysis. 2016 ; Vol. 219, No. 1. pp. 255-348.
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