Calculus of Variations and Geometric Measure Theory

D. Giovagnoli - D. Jesus - L. Silvestre

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

created by giovagnoli on 02 Oct 2025

[BibTeX]

preprint

Inserted: 2 oct 2025

Year: 2025

ArXiv: 2509.26565 PDF

Abstract:

We establish interior $C^{1,\alpha}$ regularity estimates for some $\alpha > 0$, for solutions of the fractional $p$-Laplace equation $(-\Delta_p)^s u = 0$ when $p$ is in the range $p \in [2,2/(1-s))$.