Calculus of Variations and Geometric Measure Theory

J. Ok - G. Scilla - B. Stroffolini

Regularity theory for parabolic systems with Uhlenbeck structure

created by scilla on 11 Feb 2023
modified on 12 Dec 2023


Published Paper

Inserted: 11 feb 2023
Last Updated: 12 dec 2023

Journal: Journal de Mathématiques Pures et Appliquées
Volume: 182
Pages: 116-163
Year: 2024
Doi: 10.1016/j.matpur.2023.12.003

ArXiv: 2302.05649 PDF


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 Hölder 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.

Keywords: general growth, full regularity, $\varphi$-Laplace system, Uhlenbeck-type parabolic systems