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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

n/p-harmonic maps: regularity for the sphere case

Francesca Da Lio and Armin Schikorra


We introduce $n$/$p$-harmonic maps as critical points of the energy $E(v) = \int | \Delta^{\alpha/2} v |^{p}$ where pointwise $v: D \subset \mathbb{R}^n \to \mathbb{S}^{N-1}$, for the $N$-sphere $\mathbb{S}^{N-1} \subset \mathbb{R}^N$ and $\alpha = n/p$. This energy combines the non-local behaviour of the fractional harmonic maps introduced by Riviere and first author with the degenerate arguments of the $n$-laplacian. In this setting, we will prove Hölder continuity.


Related publications

2014 Repository Open Access
Francesca Da Lio and Armin Schikorra

n/p-harmonic maps : regularity for the sphere case

In: Advances in calculus of variations, 7 (2014) 1, pp. 1-26