Regularity theory for parabolic systems with Uhlenbeck structure

Abstract

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