Calder\'on-Zygmund estimates for stochastic homogenization

TL;DR

This paper establishes probabilistic L^p estimates for the gradient of solutions to quasilinear elliptic equations with random coefficients, advancing understanding of stochastic homogenization.

Contribution

It provides the first quenched L^p estimates for gradients in stochastic homogenization of quasilinear elliptic equations.

Findings

Proved quenched L^p estimates for gradients.

Enhanced understanding of stochastic homogenization.

Applicable to quasilinear elliptic equations with random coefficients.

Abstract

We prove quenched~$L^p$--type estimates for the gradient of a solution of a quasilinear elliptic equation with random coefficients.