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arXiv · 1905.06298

C^1-Regularity of planar \infty-harmonic functions - REVISIT

Yi Ru-Ya Zhang·Yuan Zhou
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Abstract

In the seminal paper [Arch. Ration. Mech. Anal. 176 (2005), 351--361], Savin proved the $C^1$-regularity of planar $\infty$-harmonic functions $u$. Here we give a new understanding of it from a capacity viewpoint and drop several high technique arguments therein. Our argument is essentially based on a topological lemma of Savin, a flat estimate by Evans and Smart, % \cite{es11a}, $W^{1,2}_{loc}$-regularity of $|Du|$ and Crandall's flow for infinity harmonic functions.

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Yi Ru-Ya Zhang, Yuan Zhou. 2019-05-15. C^1-Regularity of planar \infty-harmonic functions - REVISIT. https://arxiv.org/abs/1905.06298

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