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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 (www.arxiv.org) 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
35/2014

Lp-gradient harmonic maps into spheres and SO(N)

Armin Schikorra

Abstract

We consider critical points of the energy $E(v) := \int_{\mathbb{R}^n} |\nabla^s v|^{\frac{n}{s}}$, where $v$ maps locally into the sphere or $SO(N)$, and $\nabla^s = (\partial_1^s,\ldots,\partial_n^s)$ is the formal fractional gradient, i.e. $\partial_\alpha^s$ is a composition of the fractional laplacian with the $\alpha$-th Riesz transform. We show that critical points of this energy are Hölder continuous.

As a special case, for $s = 1$, we obtain a new, more stable proof of Fuchs and Strzelecki's regularity result of $n$-harmonic maps into the sphere, which is interesting on its own.

Received:
15.03.14
Published:
22.04.14
MSC Codes:
58E20, 35B65, 35J60

Related publications

inJournal
2015 Repository Open Access
Armin Schikorra

Lp-gradient harmonic maps into spheres and SO(N)

In: Differential and integral equations, 28 (2015) 3/4, pp. 383-408