# American Institute of Mathematical Sciences

March  2019, 39(3): 1477-1495. doi: 10.3934/dcds.2019063

## A Hopf's lemma and the boundary regularity for the fractional p-Laplacian

 1 Department of Mathematics, South China Agricultural University, Guangzhou 510642, China 2 Department of Mathematics, Baylor University, Waco, TX 76706, USA

* Corresponding author: Yan Li

Received  January 2018 Revised  April 2018 Published  December 2018

Fund Project: The first author is partially supported by the Natural Science Foundation of China (11101160, 11271141) and the China Scholarship Council (201508440330).

We begin the paper with a Hopf's lemma for a fractional p-Laplacian problem on a half-space. Specifically speaking, we show that the derivative of the solution along the outward normal vector is strictly positive on the boundary of the half-space. Next we show that positive solutions for a fractional p-Laplacian equation possess certain Hölder continuity up to the boundary.

Citation: Lingyu Jin, Yan Li. A Hopf's lemma and the boundary regularity for the fractional p-Laplacian. Discrete & Continuous Dynamical Systems - A, 2019, 39 (3) : 1477-1495. doi: 10.3934/dcds.2019063
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