Global regularity results for a class of singular/degenerate fully nonlinear elliptic equations

TL;DR

This paper establishes regularity estimates and existence results for a class of singular and degenerate fully nonlinear elliptic equations, advancing understanding of their solutions' behavior.

Contribution

It provides the Alexandroff-Bakelman-Pucci estimate, proves global $C^{1, eta}$ regularity, and demonstrates existence of viscosity solutions for these complex equations.

Findings

Established the ABP estimate for the class of equations

Proved global $C^{1, eta}$ regularity of solutions

Proved existence of viscosity solutions to the Dirichlet problem

Abstract

We provide the Alexandroff-Bakelman-Pucci estimate and global $C^{1, \alpha}$-regularity for a class of singular/degenerate fully nonlinear elliptic equations. We also derive the existence of a viscosity solution to the Dirichlet problem with the associated operator.