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arXiv · 2509.26565

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

Davide Giovagnoli·David Jesus·Luis Silvestre
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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 $p \in [2,2/(1-s))$.

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Davide Giovagnoli, David Jesus, Luis Silvestre. 2025-09-30. $C^{1+\alpha}$ regularity for fractional $p$-harmonic functions. https://arxiv.org/abs/2509.26565

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