Work

Hölder Gradient Estimates for $(s,p)$-Poisson Equations with measurable and Hölder Data

Year: 2026

Type: preprint

Abstract: We prove interior $C^{1,α}$ estimates for weak solutions of the fractional $p$-Poisson equation, with $p\geq2$. For right-hand sides in $L^q$, we obtain the estimate when $p<(1-d/q)/(1-s)$. For $γ$-Hölder continuous right-hand sides, the range is $p<(1+γ)/(1-s)$. Both ranges of parameters are optimal.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.12012

Authors: Giovagnoli, Davide, Jesus, David

Institutions: University of Bologna, University of Parma

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

OpenAlex ID: W7221193181

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