Interior $C^{2,\alpha}$ regularity for fully nonlinear uniformly elliptic equations in dimension two

TL;DR

This paper establishes interior $C^{2,rac{ ext{alpha}}{}$ regularity for viscosity solutions of fully nonlinear uniformly elliptic equations specifically in two-dimensional spaces.

Contribution

It proves the interior $C^{2,rac{ ext{alpha}}{}$ regularity result for viscosity solutions in the two-dimensional setting, which was previously not fully understood.

Findings

Interior $C^{2,rac{ ext{alpha}}{}$ regularity is achieved for solutions.

The result applies to viscosity solutions of fully nonlinear elliptic equations.

The paper advances understanding of regularity in low-dimensional elliptic PDEs.

Abstract

In this note, we present the interior $C^{2,\alpha}$ regularity for viscosity solutions of fully nonlinear uniformly elliptic equations in dimension two.