Boundary Regularity for viscosity solutions of Fully nonlinear degenerate/singular parabolic equations

Abstract

In this paper, we establish the boundary regularity results for viscosity solutions of fully nonlinear degenerate/singular parabolic equations of the form $$u_t - x_n^{\gamma} F(D^2 u,x,t) = f,$$ where $\gamma<1$. These equations are motivated by the porous media type equations. We show the boundary $C^{1,\alpha}$-regularity of functions in their solutions class and the boundary $C^{2,\alpha}$-regularity of solutions. As an application, we derive the global regularity results and the solvability of the Cauchy-Dirichlet problems.