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

Katarzyna Mazowiecka; Michał Miśkiewicz; Patryk Tokarczuk

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arXiv · 2609.27516

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

Katarzyna Mazowiecka·Michał Miśkiewicz·Patryk Tokarczuk

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Abstract

We prove that every minimizing $p$-harmonic map from $B^3$ into $\mathbb S^3$ is locally $C^{1,α}$ for some $α\in(0,1)$, for every $p>p_0$, where $p_0=\frac{7-\sqrt{17}}{2}\approx 1.44$. This closes the gap between the previously established regularity ranges $[2,2.642]\cup[2.961,3]$ and, in particular, yields full interior regularity for all $p\ge2$. The result also extends regularity to the subquadratic range $p_0<p<2$.

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Katarzyna Mazowiecka, Michał Miśkiewicz, Patryk Tokarczuk. 2026-09-23. Regularity of minimizing $p$-harmonic maps from $B^3$ to $\mathbb{S}^3$. https://arxiv.org/abs/2609.27516

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