Sub-solutions and a point-wise Hopf's Lemma for Fractional p-Laplacian

Abstract

In this article, we prove that (−∆)+ . And we then introduce a Hopf's theorem for u ∈ C 1,1 loc ∩ L sp by subsolution and comparison principle method.

Hopf's lemmas for parabolic fractional Laplacians and parabolic fractional $p$-Laplacians

“…χ D (x) be as defined in (2.11) and η(t) ∈ C ∞ 0 ([0, T ]) satisfies (2.12). By a result in [27], we have…”