Summary
We consider weak solutions u∈Lp([0,T], W 1p (Ω))∩([0,T],L2(Ω))of the degenerate parabolic (model) -system
By local techniques it is proved, using sequences of time-space cylinders, which are adjusted to the alternative whether one is at a point of degeneracy or not, that the spatial gradient of u is α- Höldercontinuous on compact subsets of Ω× [0,T] with some α which depends only on N and p.
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Wiegner, M. On 385-01385-01385-01regularity of the gradient of solutions of degenerate parabolic systems. Annali di Matematica pura ed applicata 145, 385–405 (1986). https://doi.org/10.1007/BF01790549
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DOI: https://doi.org/10.1007/BF01790549