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MiS Preprint

Integro-differential harmonic maps into spheres

Armin Schikorra


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.

MSC Codes:
58E20, 35B65, 35J60, 35S0

Related publications

2015 Journal Open Access
Armin Schikorra

Integro-differential harmonic maps into spheres

In: Communications in partial differential equations, 40 (2015) 3, pp. 506-539