$C^{1+\hat{I}\pm }$ regularity for fractional $p$-harmonic functions

Abstract

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