Gradient regularity for fully nonlinear equations with degenerate coefficients

TL;DR

This paper establishes $C^{1,eta}$ regularity estimates for viscosity solutions of fully nonlinear equations that degenerate along a hypersurface, advancing understanding of solution smoothness in degenerate contexts.

Contribution

It provides new $C^{1,eta}$ regularity results for fully nonlinear degenerate equations, extending classical regularity theory to degenerate cases.

Findings

Established $C^{1,eta}$ estimates for degenerate fully nonlinear equations.

Extended regularity theory to include equations degenerating on hypersurfaces.

Provided a framework for analyzing viscosity solutions with degeneracies.

Abstract

We derive $C^{1,\alpha}$ estimates for viscosity solutions of fully nonlinear equations degenerating on a hypersurface.