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 language | English (US) |
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Pages (from-to) | 255-348 |
Number of pages | 94 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 219 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1 2016 |
ASJC Scopus subject areas
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering