Twice differentiability of solutions to fully nonlinear parabolic equations near the boundary

Abstract

In this paper, we prove ${\mathcal{H}}^{2+\alpha }$ regularity for viscosity solutions to non-convex fully nonlinear parabolic equations near the boundary. This constitutes the parabolic counterpart of a similar $C^{2,\alpha }$ regularity result due to Silvestre and Sirakov proved in [15] for solutions to non-convex fully nonlinear elliptic equations.