Local and global $C^{1,\beta}$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type

TL;DR

This paper proves gradient Hölder continuity for solutions to a broad class of uniformly elliptic quasilinear equations, including p-Laplace and Orlicz-Laplace types, improving existing regularity results both inside the domain and at the boundary.

Contribution

It establishes new gradient regularity results for quasilinear elliptic equations of p-Laplace and Orlicz-Laplace types, extending and refining previous findings.

Findings

Gradient Hölder continuity in the interior

Gradient regularity up to the boundary

Applicable to Dirichlet and Neumann boundary conditions

Abstract

We establish gradient H\"older continuity for solutions to quasilinear, uniformly elliptic equations, including $p$-Laplace and Orlicz-Laplace type operators. We revisit and improve upon the results existing in the literature, proving gradient regularity both in the interior and up to the boundary, under Dirichlet or Neumann boundary conditions.