Integro-differential harmonic maps into spheres
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Submission date: 29. Jan. 2014
published in: Communications in partial differential equations, 40 (2015) 3, p. 506-539
DOI number (of the published article): 10.1080/03605302.2014.974059
MSC-Numbers: 58E20, 35B65, 35J60, 35S0
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We introduce (integro-differential) harmonic maps into spheres, which are deﬁned as critical points of the Besov-Slobodeckij energy ∫ Ω ∫ Ωdxdy. For ps = 2 these are the classical fractional harmonic maps ﬁrst considered by Da Lio and Riviere. For ps ⁄= 2 this is a new energy which has degenerate, non-local Euler-Lagrange equations. For the critical case, ps = n∕s, we show Holder continuity of these maps.