C^{1,\alpha} regularity for a class of singular/degenerate fully nonlinear elliptic equations with oblique boundary conditions

TL;DR

This paper proves global C^{1, alpha} regularity for viscosity solutions of a broad class of singular and degenerate fully nonlinear elliptic equations with oblique boundary conditions, extending previous results.

Contribution

It extends existing regularity results to include a wider class of singular and degenerate equations with oblique boundary conditions.

Findings

Established global C^{1, alpha} regularity for solutions.

Extended previous results to singular cases.

Broadened the class of equations with proven regularity.

Abstract

In this paper, we establish global $C^{1, \alpha}$ regularity for viscosity solutions to a class of singular and degenerate fully nonlinear elliptic equations subject to oblique boundary conditions. Our work extends the findings in \cite{BKO25} to a broader class of equations, notably encompassing the singular case.