Boundary regularity and Hopf lemma for nondegenerate stable operators

2024/10/01 by Florian Grube, Grube, Florian · 3 citations
Computer Science · Engineering · Mathematics · #35B65 #35R09 #35S15 #47G20 #60G52 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2410.00829

openalex publication_date 2024/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove sharp boundary Hölder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior C^1,dini-property. This result is new even for the fractional Laplacian. A Hopf-type boundary lemma is proven, too. An additional feature of this work is that the regularity estimate is robust as s→ 1- and we recover the classical results for second order equations.

Cited by

• Abnormal boundary decay for stable operators
• The inhomogeneous fractional Dirichlet problem
• Nonlinear nonlocal equations in Reifenberg flat domains

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