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

TL;DR

This paper proves optimal regularity results for solutions of certain degenerate or singular fully nonlinear elliptic equations, identifying minimal conditions on the operators involved.

Contribution

It introduces the minimal regularity conditions needed on the operator to achieve C^{1,eta} regularity for viscosity solutions.

Findings

Established C^{1,eta} regularity under minimal assumptions

Identified optimal regularity conditions for operators

Extended regularity theory to degenerate/singular equations

Abstract

We establish an optimal C^{1,\alpha}-regularity for viscosity solutions of degenerate/singular fully nonlinear elliptic equations by finding minimal regularity requirements on the associated operator.