Publications
2012
Issue 43

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 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

43/2012

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

Francesca Da Lio and Armin Schikorra

Abstract

We introduce $n$ / $p$ -harmonic maps as critical points of the energy $E (v) = \int | Δ^{α / 2} v |^{p}$ where pointwise $v : D \subset R^{n} \to S^{N - 1}$ , for the $N$ -sphere $S^{N - 1} \subset R^{N}$ and $α = n / p$ . 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.

Contact the author per mail Download full preprint 387 KB

Received:: 17.07.12

Published:: 17.07.12

Related publications

inJournal

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

BibTex DOI: 10.1515/acv-2012-0107 ArXiv: 1202.1151