A Hopf's lemma and a strong minimum principle for the fractional $p$-Laplacian

Abstract

Our propose here is to provide a Hopf Lemma and a strong minimum principle for week supersolutions of \[ (-Δ_p)^s u= c(x)|u|^{p-2}u \quad \text{ in } Ω\] where $\Omega$ is an open set of ${\mathbb{R}}^N,$ $s\in (0,1),$ $p\in (1,+\infty ),$ $c\in C(\overline{\Omega })$ and $(-{\Delta }_p{)}^s$ is the fractional $p$-Laplacian.

12 pages

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