Interpolated time-Hölder regularity of solutions of fully nonlinear parabolic equations

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 $\min\{\inf_βL_βu,\sup_γL_γu\}-\partial_t u=0$, where $L_β,L_γ$ 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.

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