Further time regularity for fully non-linear parabolic equations

TL;DR

This paper proves new H"older continuity estimates for the time derivatives of solutions to fully non-linear parabolic equations, even when classical second derivative regularity is unavailable.

Contribution

It introduces novel regularity results for the time derivatives of solutions to fully non-linear parabolic equations without requiring $C^{2,eta}$ estimates.

Findings

Established H"older estimates for time derivatives

Extended regularity theory to equations lacking classical second derivative bounds

Provided new tools for analyzing fully non-linear parabolic equations

Abstract

We establish H\"older estimates for the time derivative of solutions of fully non-linear parabolic equations that does not necessarily have $C^{2,\alpha}$ estimates.