Regularity for parabolic systems of Uhlenbeck type with Orlicz growth

Lars Diening; Toni Scharle; Sebastian Schwarzacher

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arXiv · 1603.05604

Regularity for parabolic systems of Uhlenbeck type with Orlicz growth

Lars Diening·Toni Scharle·Sebastian Schwarzacher

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Abstract

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 has Uhlenbeck structure of Orlicz type. This paper closes the gap of [22] where Liebermann proved that if the gradient of a solution is bounded, it is H\"older 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.

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Lars Diening, Toni Scharle, Sebastian Schwarzacher. 2016-03-17. Regularity for parabolic systems of Uhlenbeck type with Orlicz growth. https://arxiv.org/abs/1603.05604

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