A Hopf's Lemma and the Boundary Regularity for the Fractional P-Laplacian

Lingyu Jin; Yan Li

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arXiv · 1711.02707

A Hopf's Lemma and the Boundary Regularity for the Fractional P-Laplacian

Lingyu Jin·Yan Li

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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 to a fractional p-Laplacian equation possess certain Holder continuity up to the boundary.

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Lingyu Jin, Yan Li. 2017-11-07. A Hopf's Lemma and the Boundary Regularity for the Fractional P-Laplacian. https://arxiv.org/abs/1711.02707

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