C^1+α regularity for fractional p-harmonic functions

2025/09/30 by Giovagnoli, Davide, Jesus, David, Silvestre, Luis
#35B65 #35J70 #35R09 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.26565

Abstract

We establish interior C^1,α regularity estimates for some α> 0, for solutions of the fractional p-Laplace equation (-Δ_p)^s u = 0 when p is in the range p ∈ [2,2/(1-s)).

Citations

• Higher Hölder regularity for fractional (p,q)-Laplace equations
• Improved Hölder regularity of fractional (p,q)-Poisson equation with regular data
• Lipschitz regularity of fractional p-Laplacian
• Gradient estimates for the fractional p-Poisson equation
• A survey on boundary regularity for the fractional p-Laplacian and its applications
• Gradient regularity for (s,p)-harmonic functions
• Higher differentiability for the fractional p-Laplacian
• Higher Hölder regularity for the fractional p-Laplace equation in the subquadratic case
• Calderón-Zygmund estimates for the fractional p-Laplacian
• Gradient regularity and first-order potential estimates for a class of nonlocal equations
• Coercivity estimates for integro-differential operators
• Fractional thoughts
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• Equivalence of solutions to fractional p-Laplace type equations
• Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case
• Global Hölder regularity for the fractional p-Laplacian
• Nonlocal Harnack inequalities
• Nonlocal Harnack inequalities
• Hölder estimates for viscosity solutions of equations of fractional p-Laplace type
• Regularity results for nonlocal parabolic equations
• Non-local gradient dependent operators

Related

• Limited regularity of solutions to fractional heat and Schrödinger equations
• Lipschitz regularity of fractional p-Laplacian
• Higher Hölder regularity for the fractional p-Laplace equation in the subquadratic case
• Fine Boundary Regularity For The Fractional (p,q)-Laplacian
• Boundary regularity for the fractional heat equation