Integro-differential harmonic maps into spheres

We introduce (integro-differential) harmonic maps into spheres, which are defined as critical points of the Besov-Slobodeckij energy $\int\limits_{\Omega}\int\limits_{\Omega} \frac{|v(x)-v(y)|^{p_s}}{|x-y|^{n+sp_s}}\ dx\ dy$\mathrm{.}For$p_s = 2$ these are the classical fractional harmonic maps first considered by Da Lio and Riviere. For $p_s\mathrm{\ne }2$ this is a new energy which has degenerate, non-local Euler-Lagrange equations. For the critical case, $p_s=n\mathrm{/}s$, we show Holder continuity of these maps.