Mathematics > Analysis of PDEs
[Submitted on 7 May 2018 (v1), last revised 16 May 2018 (this version, v2)]
Title:A Hopf lemma and regularity for fractional $p-$Laplacians
View PDFAbstract: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 $u$.
Submission history
From: Shijie Qi [view email][v1] Mon, 7 May 2018 23:15:44 UTC (14 KB)
[v2] Wed, 16 May 2018 12:32:13 UTC (14 KB)
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