Hölder extension for fractional Laplacian

2025/08/16 by Feng Li, Li, Feng
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2508.12134

openalex publication_date 2025/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we characterize the sharp boundary condition such that the fractional harmonic extensions with Hölder regularity up to the boundary is globally Hölder continuous. The proofs are based on estimates of fractional harmonic measure decay and uniform fractional fatness of the complement of the domain.

Citations

• Boundary estimates and a Wiener criterion for the fractional Laplacian
• Asymptotic behavior of nonlocal p-Rayleigh quotients
• Boundary Hölder Regularity for Elliptic Equations
• Higher H "older regularity for the fractional p-Laplacian in the\n superquadratic case
• Fractional superharmonic functions and the Perron method for nonlinear\n integro-differential equations
• Perron's Method and Wiener's Theorem for a Nonlocal Equation
• Global regularity for the free boundary in the obstacle problem for the fractional Laplacian
• Global Hölder regularity for the fractional p-Laplacian
• Existence results for fractional p-Laplacian problems via Morse theory
• The fractional Cheeger problem
• The Pohozaev identity for the fractional Laplacian
• The Pohozaev Identity for the Fractional Laplacian
• The Dirichlet problem for the fractional Laplacian: regularity up to the\n boundary
• Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian

Related

• Hölder regularity for the fractional p-Laplacian, revisited
• Global Hölder regularity for the fractional p-Laplacian
• Fractional Laplacians and extension problems: the higher rank case
• Global Hölder regularity for eigenfunctions of the fractional g-Laplacian
• Higher H "older regularity for the fractional p-Laplacian in the\n superquadratic case