# Optimal C^{1,\apha} regularity for degenerate fully nonlinear elliptic equations with Neumann boundary condition

## TL;DR

This paper establishes sharp C^{1,eta} regularity results for viscosity solutions of degenerate fully nonlinear elliptic equations with Neumann boundary conditions, advancing understanding of boundary regularity in such equations.

## Contribution

It provides the first sharp boundary regularity results for degenerate fully nonlinear elliptic equations with Neumann boundary conditions.

## Key findings

- Sharp C^{1,eta} regularity at the boundary.
- Extension of regularity theory to degenerate equations.
- New techniques for boundary regularity analysis.

## Abstract

In the present paper, we study sharp C^{1;\alpha} regularity results with boundary Neumann condition for viscosity solutions for a class of degenerate fully non-linear elliptic equations with Neumann boundary conditions.