Regularity for parabolic systems of Uhlenbeck type with Orlicz growth

Abstrakt

We study the local regularity of p-caloric functions or more generally of phi-caloric functions. In particular, we study local solutions of non-linear parabolic systems with homogeneous right hand side, where the leading terms have Uhlenbeck structure of Orlicz type.

This paper closes the gap of [23] where Liebermann proved that if the gradient of a solution is bounded, it is Holder continuous. The crucial step is a novel local estimates for the gradient of the solutions, which generalize and improve the pioneering estimates of DiBenedetto and Friedman [12,10] for the p-Laplace heat equation. (C) 2018 Published by Elsevier Inc.

Klíčová slova

• Non-linear PDE's
• Degenerate parabolic systems
• Gradient estimates
• De Giorgi technique