Regularity theory for parabolic systems with Uhlenbeck structure

We establish local regularity theory for parabolic systems of Uhlenbeck type with phi-growth. In particular, we prove local boundedness of weak solutions and their gradient, and then local Holder continuity of the gradients, providing suitable assumptions on the growth function phi. Our approach, being independent of the degeneracy of the system, allows for a unified treatment of both the degenerate and the singular case.(c) 2023 Elsevier Masson SAS. All rights reserved.