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In this manuscript, we derive Schauder estimates for viscosity solutions tonon-convex fully nonlinear second-order parabolic equations \[ \partial_t u -F(x, t,D^2u) = f (x, t) \quad \text{in} \quad \mathrm{Q}_1 = B_1 \times (-1,0], \] provided that the source $f$ and the coefficients of $F$ are H\"{o}ldercontinuous functions and $F$ enjoys a small ellipticity aperture. Furthermore,for problems with merely bounded data, we prove that such solutions are $C^{1,\text{Log-Lip}}$ smooth in the parabolic metric. We also addressCalder\'{o}n-Zygmund estimates for such a class of non-convex operators.Finally, we connect our findings with recent estimates for fully nonlinearmodels in certain solution classes.

Schauder and Calder\'on-Zygmund type estimates for fully nonlinear parabolic equations under "small ellipticity aperture" and applications