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.

30 pages