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

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.