# Regularity for parabolic systems of Uhlenbeck type with Orlicz growth

Diening L, Scharle T, Schwarzacher S (2016)
arXiv:1603.05604.

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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 term has Uhlenbeck structure of Orlicz type. We show that gradients of these solutions are locally bounded. This closes the gap to earlier works and thus implies that gradients of these solutions are locally H\"older continuous.
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Diening L, Scharle T, Schwarzacher S. Regularity for parabolic systems of Uhlenbeck type with Orlicz growth. arXiv:1603.05604. 2016.
Diening, L., Scharle, T., & Schwarzacher, S. (2016). Regularity for parabolic systems of Uhlenbeck type with Orlicz growth. arXiv:1603.05604
Diening, L., Scharle, T., and Schwarzacher, S. (2016). Regularity for parabolic systems of Uhlenbeck type with Orlicz growth. arXiv:1603.05604.
Diening, L., Scharle, T., & Schwarzacher, S., 2016. Regularity for parabolic systems of Uhlenbeck type with Orlicz growth. arXiv:1603.05604.
L. Diening, T. Scharle, and S. Schwarzacher, “Regularity for parabolic systems of Uhlenbeck type with Orlicz growth”, arXiv:1603.05604, 2016.
Diening, L., Scharle, T., Schwarzacher, S.: Regularity for parabolic systems of Uhlenbeck type with Orlicz growth. arXiv:1603.05604. (2016).
Diening, Lars, Scharle, Toni, and Schwarzacher, Sebastian. “Regularity for parabolic systems of Uhlenbeck type with Orlicz growth”. arXiv:1603.05604 (2016).
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arXiv 1603.05604