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

Carlo Alberto Antonini

doi:10.1016/j.na.2026.114266

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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Carlo Alberto Antonini

DOI: 10.1016/j.na.2026.114266

Cited by: 0

Abstract

We establish gradient Hölder 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.

Fields of Study & Subjects

Nonlinear Partial Differential Equations Geometric Analysis and Curvature Flows Advanced Harmonic Analysis Research

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 12 January 2026
Document type: Preprint