$C^{2,\alpha}$ estimates for nonlinear elliptic equations of twisted type

TL;DR

This paper establishes interior $C^{2,eta}$ regularity estimates for solutions to a class of fully nonlinear elliptic equations of twisted type, including convex plus concave equations, with applications to elliptic regularization and Monge-Ampère equations.

Contribution

It provides the first a priori $C^{2,eta}$ estimates for twisted type equations, extending regularity theory to new classes of nonlinear elliptic PDEs.

Findings

Proves interior $C^{2,eta}$ estimates for twisted type equations.

Applies results to elliptic regularization and Monge-Ampère equations.

Provides a new proof of Streets-Warren estimate.

Abstract

We prove a priori interior $C^{2,\alpha}$ estimates for solutions of fully nonlinear elliptic equations of twisted type. For example, our estimates apply to equations of the type convex + concave. These results are particularly well suited to equations arising from elliptic regularization. As application, we obtain a new proof of an estimate of Streets-Warren on the twisted real Monge-Ampere equation.