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

Lingyu Jin; Yan Li

doi:10.3934/dcds.2019063

Article Contents

2019, Volume 39, Issue 3: 1477-1495. Doi: 10.3934/dcds.2019063

This issue Previous Article Classification for positive solutions of degenerate elliptic system Next Article On finite energy solutions of fractional order equations of the Choquard type

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

Lingyu Jin^1, and
Yan Li^2, ,

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
* Corresponding author: Yan Li

Received: December 31, 2017

Revised: March 31, 2018

Published: December 2018

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 35S05, 35B50, 35B65; Secondary: 35B09.

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