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

We consider vector valued weak solutions u: T RN with N N of degenerate or singular parabolic systems of type equation* ₜ u - div \, a (z, u, Du) = 0 T= (0, T), equation* where denotes an open set in R^n 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, ) is H\"older continuous for every R^Nn, 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.