A Hopf's lemma and the boundary regularity for the fractional p-Laplacian
Lingyu Jin, Yan Li · Discrete and Continuous Dynamical Systems · 2018
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.