English

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

Analysis of PDEs 2025-04-29 v2

Abstract

In this manuscript, we provide local LqL^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 LqL^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.

Keywords

Cite

@article{arxiv.2504.18401,
  title  = {Regularity for monotone Operators and applications to homogenization of $p$-Laplace type equations},
  author = {Lukas Koch and Mathias Schäffner},
  journal= {arXiv preprint arXiv:2504.18401},
  year   = {2025}
}