Gradient estimates for the fractional p-Poisson equation

2025/03/07 by Bögelein, Verena, Duzaar, Frank, Liao, Naian +1 · 4 citations
#35B65 #35J60 #35R09 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.05903

Abstract

We consider local weak solutions to the fractional p-Poisson equation of order s, i.e. ( - Δ_p)^s u = f. In the range p>1 and s∈ ((p-1)/(p),1) we prove Calderón & Zygmund type estimates at the gradient level. More precisely, we show for any q>1 that f∈ L^(qp)/(p-1)_{\rm loc} \Longrightarrow ∇ u∈ L^qp_{\rm loc}. The qualitative result is accompanied by a local quantitative estimate.

Cited by

• C^1+α regularity for fractional p-harmonic functions
• On boundary regularity for the fractional p-Laplacian with unbounded reactions
• Nonlinear nonlocal equations in Reifenberg flat domains
• Improved Hölder regularity of fractional (p,q)-Poisson equation with regular data

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