Boundary regularity for viscosity solutions of fully nonlinear degenerate/singular parabolic equations.

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 γ F (D 2 u , x , t) = f , where γ < 1 . These equations are motivated by the porous media type or fast diffusion type equations. We show the boundary C 1 , α -regularity of functions in their solutions class and the boundary C 2 , α -regularity of viscosity solutions. As an application, we derive the global regularity results and the solvability of the Cauchy–Dirichlet problems. [ABSTRACT FROM AUTHOR]