Fine boundary regularity for the singular fractional p-Laplacian

2024/02/04 by Antonio Iannizzotto, Sunra Mosconi, Iannizzotto, Antonio +1 · 5 citations
Computer Science · Mathematics · #35D10 #35R11 #47G20 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2402.02448

openalex publication_date 2024/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the boundary weighted regularity of weak solutions u to a s-fractional p-Laplacian equation in a bounded smooth domain Ω with bounded reaction and nonlocal Dirichlet type boundary condition, in the singular case p∈(1,2) and with s∈(0,1). We prove that u/\rm d_Ω^s has a α-Hölder continuous extension to the closure of Ω, \rm d_Ω(x) meaning the distance of x from the complement of Ω. This result corresponds to that of ref. [28] for the degenerate case p≥ 2.

Cited by

• Finite Elements with weighted bases for the fractional Laplacian
• The inhomogeneous fractional Dirichlet problem
• On boundary regularity for the fractional p-Laplacian with unbounded reactions
• Higher Hölder regularity for fractional (p,q)-Laplace equations
• Nonlinear nonlocal equations in Reifenberg flat domains

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