Hölder gradient estimates for a class of singular or degenerate parabolic equations

We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic equation u_{t}=\lvert\nabla u\rvert^{\kappa}\operatorname{div}(\lvert\nabla u\rvert^{p-% 2}\nabla u), where {p\in(1,\infty)} and {\kappa\in(1-p,\infty)} . This includes the from {L^{\infty}} to {C^{1,\alpha}} regularity for parabolic p-Laplacian equations in both divergence form with {\kappa=0} , and non-divergence form with {\kappa=2-p} .