Regularity for radial solutions of degenerate fully nonlinear equations

TL;DR

This paper establishes Holder regularity of the derivatives of radial solutions to a class of degenerate fully nonlinear equations characterized by specific homogeneity and ellipticity conditions.

Contribution

It proves regularity results for radial solutions of a broad class of degenerate fully nonlinear equations with specific homogeneity properties.

Findings

Holder regularity of derivatives established

Applicable to Hessian-type operators with degree 1 homogeneity in Hessian

Results extend understanding of degenerate fully nonlinear equations

Abstract

In this paper we prove Holder regularity of the derivative of radial solutions to fully nonlinear equations when the operator is hessian, homogenous of degree 1 in the Hessian, homogenous of some degree $\alpha>-1$ in the gradient and which is elliptic when the gradient is not null.