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arXiv · 1805.02776

A Hopf lemma and regularity for fractional $p-$Laplacians

Wenxiong Chen·Congming Li·Shijie Qi
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Abstract

In this paper, we study qualitative properties of the fractional $p$-Laplacian. Specifically, we establish a Hopf type lemma for positive weak super-solutions of the fractional $p-$Laplacian equation with Dirichlet condition. Moreover, an optimal condition is obtained to ensure $(-\triangle)_p^s u\in C^1(\mathbb{R}^n)$ for smooth functions $u$.

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Wenxiong Chen, Congming Li, Shijie Qi. 2018-05-07. A Hopf lemma and regularity for fractional $p-$Laplacians. https://arxiv.org/abs/1805.02776

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