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 \(\begin{aligned} u_{t} - x_{n}^{\gamma } F(D^{2} u,x,t) = f, \end{aligned}\) $$\begin{array}{c}\hfill u_t-x_n^{\gamma }F(D^{2}u,x,t)=f,\end{array}$$ where \(\gamma <1\) $\gamma <1$ . These equations are motivated by the porous media type or fast diffusion type equations. We show the boundary \(C^{1,\alpha }\) $C^{1,\alpha }$ -regularity of functions in their solutions class and the boundary \(C^{2,\alpha }\) $C^{2,\alpha }$ -regularity of viscosity solutions. As an application, we derive the global regularity results and the solvability of the Cauchy–Dirichlet problems.