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arXiv · 2302.05649

Regularity theory for parabolic systems with Uhlenbeck structure

Jihoon Ok·Giovanni Scilla·Bianca Stroffolini
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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.

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Jihoon Ok, Giovanni Scilla, Bianca Stroffolini. 2023-02-11. Regularity theory for parabolic systems with Uhlenbeck structure. https://arxiv.org/abs/2302.05649

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