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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Nonlinear Partial Differential Equations
Numerical methods in inverse problems
Publication details
- Journal / source
- Communications in Partial Differential Equations
- Publisher
- Informa UK Limited
- Volume
- 51
- Issue
- 7
- Pages
- 730–791
- Publication date
- 3 July 2026
- Language
- EN