Regularity for monotone Operators and applications to homogenization of $p$-Laplace type equations

Abstract

In this manuscript, we provide local $L^q$-estimates for the gradient of solutions of a class of quasilinear equations whose principal part lacks strong monotonicity. These estimates are used to establish uniform large-scale $L^q$-estimates for the gradient of solutions of degenerate/singular quasilinear equations with oscillating coefficients and large-scale Lipschitz estimates for solutions of non-degenerate equations.

v2. Minor revisions. Accepted for publication in Communications in PDE