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

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