Integro-differential harmonic maps into spheres

Abstract

We introduce (integro-differential) harmonic maps into spheres, which are defined as critical points of the Besov-Slobodeckij energy $\underset{\Omega }{\int }\underset{\Omega }{\int }\frac{|v(x)-v(y){|}^{p_s}}{|x-y{|}^{n+s{p}_s}}dxdy$. For $p_s=2$ these are the classical fractional harmonic maps first considered by Da Lio and Riviere. For $p_s\ne 2$ 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.

References in corpus (1)

• n/p-Harmonic maps: regularity for the sphere case

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