H\"older regularity of the gradient for solutions of fully nonlinear equations with sublinear first order terms

TL;DR

This paper proves that solutions to certain fully nonlinear equations with sublinear first order terms have gradients that are locally H"older continuous, both inside the domain and near the boundary.

Contribution

It establishes new regularity results for solutions of fully nonlinear equations with sublinear first order terms, including boundary regularity.

Findings

Gradient of solutions is locally H"older continuous

Regularity holds both in interior and boundary regions

Advances understanding of nonlinear PDE regularity

Abstract

In this paper we shall establish some regularity results of solutions of a class of fully nonlinear equations, with a first order term which is sub-linear. We prove local H\"older regularity of the gradient both in the interior and up to the boundary.