Hopf's lemmas and boundary point results for the fractional p-Laplacian

2023/12/12 by Ochoa, Pablo, Salort, Ariel
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.07734

Abstract

In this paper, we consider different versions of the classical Hopf's boundary lemma in the setting of the fractional p-Laplacian for p ≥ 2. We start by providing for a new proof to a Hopf's lemma based on comparison principles. Afterwards, we give a Hopf's result for sign-changing potential describing the behavior of the fractional normal derivative of solutions around boundary points. The main contribution here is that we do not need to impose a global condition on the sign of the solution. Applications of the main results to boundary point lemmas and non-local non-linear overdetermined problems are also provided.

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