# The Neumann problem for a class of fully nonlinear elliptic partial differential equations

## TL;DR

This paper develops global second-order derivative estimates and proves the existence of admissible solutions for the Neumann problem associated with a class of fully nonlinear elliptic PDEs, advancing understanding of boundary value problems.

## Contribution

It introduces new global $C^2$ estimates and employs the method of continuity to establish existence results for fully nonlinear elliptic equations with Neumann boundary conditions.

## Key findings

- Established global $C^2$ estimates for the Neumann problem.
- Proved existence of $k$-admissible solutions using the method of continuity.
- Extended the theory of boundary value problems for nonlinear elliptic equations.

## Abstract

In this paper, we establish a global $C^2$ estimates to the Neumann problem for a class of fullly nonlinear elliptic equations. By the method of continuity, we establish the existence theorem of $k$-admissible solutions of the Neumann problems.