Interpolated time-Hölder 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 Hölder 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.