A note on Hopf's lemma and strong minimum principle for nonlocal equations with non-standard growth

2022/08/29 by Abhrojyoti Sen, Sen, Abhrojyoti
Mathematics · #35B50 #35D30 #35R11 #47G20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2208.13498

openalex publication_date 2022/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω⊂ ℝⁿ be any open set and u be a weak supersolution of Lu=c(x)g(|u|)(u)/(|u|) where Lu(x)=p.v. ∫_ℝⁿ g((|u(x)-u(y)|)/(|x-y|^s)) (u(x)-u(y))/(|u(x)-u(y)|) K(x,y)(dy)/(|x-y|^s) and g=G^′ for some Young function G. This note imparts a Hopf's type lemma and strong minimum principle for u when c(x) is continuous in Ω that extend the results of Del Pezzo and Quaas (JDE-2017) in fractional Orlicz-Sobolev setting.

Related

• On Hopf's Lemma and the Strong Maximum Principle
• On the strong maximum principle for nonlocal operators
• On Hopf's Lemma for sign-changing supersolutions to fractional Laplacian equations
• Hopf type lemmas for subsolutions of integro-differential equations
• Hopf's lemmas and boundary behaviour of solutions to the fractional Laplacian in Orlicz-Sobolev spaces