Schauder and Calderón–Zygmund type estimates for fully nonlinear parabolic equations under “small ellipticity aperture” and applications

Abstract

In this manuscript, we derive some Schauder estimates for viscosity solutions to non-convex fully nonlinear second-order parabolic equations of the form: ∂tu−F(x,t,D2u)=f(x,t)inQ1=B1×(−1,0],provided that the source f and the coefficients of F are Hólder continuous functions, and F enjoys a small ellipticity aperture. Furthermore, for problems with merely bounded data, we prove that such solutions are C1,Log-Lip-regular. We also obtain Calderón-Zygmund estimates for such a class of non-convex operators. Finally, we connect our results and recent estimates for fully nonlinear models in certain solution classes.