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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.
