Regularity theory for parabolic systems with Uhlenbeck structure

Abstract

We establish local regularity theory for parabolic systems of Uhlenbeck type with φ-growth. In particular, we prove local boundedness of weak solutions and their gradient, and then local Hölder continuity of the gradients, providing suitable assumptions on the growth function φ. Our approach, being independent of the degeneracy of the system, allows for a unified treatment of both the degenerate and the singular case.