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

2019/04/30 by Zaizheng Li, Qidi Zhang, Li, Zaizheng +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1905.00127

openalex publication_date 2019/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a Hopf's lemma in the point-wise sense. The essential technique is to prove (-Δ)^s_p u(x) is uniformly bounded in the unit ball B₁⊂ℝⁿ, where u(x)=(1-|x|²)^s₊. Also we study the global Hölder continuity of bounded positive solutions for (-Δ)^s_p u(x)=f(x,u).

Citations

• Non-local gradient dependent operators
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Hitchhiker's guide to the fractional Sobolev spaces
• A direct method of moving spheres on fractional order equations

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