Partial gradient regularity for parabolic systems with degenerate diffusion and Hölder continuous coefficients

We consider vector valued weak solutions $u:{\mathrm{\Omega }}_T\to {\mathbb{R}}^N$ with $N\in \mathbb{N}$ of degenerate or singular parabolic systems of type \begin{equation*} \partial_t u - $\mathrm{d}\mathrm{i}\mathrm{v}$ , a(z,u,Du) = 0 \qquad$\text{in}$\qquad Ω_T= Ω\times (0,T), \end{equation*} where $\mathrm{\Omega }$ denotes an open set in ${\mathbb{R}}^n$ for $n\ge 1$ and $T>0$ a finite time. Assuming that the vector field $a$ is not of Uhlenbeck-type structure, satisfies $p$-growth assumptions and $(z,u)\mapsto a(z,u,\xi )$ is Hölder continuous for every $\xi \in {\mathbb{R}}^{Nn}$, we show that the gradient $Du$ is partially Hölder continuous, provided the vector field degenerates like that of the $p$-Laplacian for small gradients.