Partial gradient regularity for parabolic systems with degenerate diffusion and H\"older continuous coefficients

We consider vector valued weak solutions u:ΩT→ RN with N∈ N of degenerate or singular parabolic systems of type {equation*} ∂_t u - div \, a(z,u,Du) = 0 Ω_T= Ω× (0,T), {equation*} where Ω denotes an open set in Rⁿ for n≥ 1 and $T>0$ a finite time. Assuming that the vector field a is not of Uhlenbeck-type structure, satisfies p-growth assumptions and (z,u)↦ a(z,u,ξ) is H\"older continuous for every ξ∈ RNn, we show that the gradient $Du$ is partially H\"older continuous, provided the vector field degenerates like that of the p-Laplacian for small gradients.