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
6/2014
Integro-differential harmonic maps into spheres
Armin Schikorra
Abstract
We introduce (integro-differential) harmonic maps into spheres, which are defined as critical points of the Besov-Slobodeckij energy $$\int_\Omega \int_\Omega \frac{|u(x)-u(y)|^{p_s}}{|x-y|^{n+sp_s}}dx dy.$$For $p_s=2$ these are the classical fractional harmonic maps first considered by Da Lio and Riviere. For $p_s \not = 2$ this is a new energy which has degenerate, non-local Euler-Lagrange equations. For the critical case, $p_s= n/s$, we show Holder continuity of these maps.