Interpolated time-H\"older regularity of solutions of fully nonlinear parabolic equations

TL;DR

This paper establishes interior Schauder estimates and Evans-Krylov regularity results for a class of fully nonlinear parabolic Isaacs equations, advancing the understanding of their regularity properties.

Contribution

It provides new interior regularity estimates for fully nonlinear parabolic Isaacs equations using the maximum principle and extends Evans-Krylov theory to these equations.

Findings

Established interior Schauder estimates for Isaacs equations

Proved Evans-Krylov theorem for fully nonlinear parabolic equations

Extended regularity results to equations with variable H"older coefficients

Abstract

We show interior Schauder estimates for a special class of fully nonlinear parabolic Isaacs equations by the maximum principle, providing an Evans-Krylov result for the model equation $\min\{\inf_{\beta}L_\beta u,\sup_\gamma L_\gamma u\}-\partial_t u=0$, where $L_\beta,L_\gamma$ are linear operators with possibly variable H\"older coefficients. We also give a proof of the Evans-Krylov theorem for fully nonlinear uniformly parabolic equations for which a regularity theory of the stationary non-homogeneous equation is available.