Regularity of minimizing $p$-harmonic maps from $B^3$ to ${\mathbb{S}}^3$

Katarzyna Mazowiecka, Michał Miśkiewicz, Patryk Tokarczuk

We prove that every minimizing $p$-harmonic map from $B^3$ into ${\mathbb{S}}^3$ is locally $C^{1,\alpha }$ for some $\alpha \in (0,1)$, for every $p>p_0$, where $p_0=\frac{7-\sqrt{17}}{2}\approx…