Fully nonlinear parabolic equations in two space variables

TL;DR

This paper establishes H"older estimates for second derivatives of solutions to fully nonlinear parabolic equations in two variables, extending the regularity theory to higher dimensions.

Contribution

It introduces techniques to prove regularity estimates for fully nonlinear parabolic equations, applicable in two and higher dimensions.

Findings

Proved H"older estimates for second derivatives in two variables.

Extended regularity theory to higher-dimensional fully nonlinear parabolic equations.

Abstract

H\"older estimates for second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.