Preprint 6/2014

Integro-differential harmonic maps into spheres

Armin Schikorra

Contact the author: Please use for correspondence this email.
Submission date: 29. Jan. 2014
Pages: 46
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
Download full preprint: PDF (538 kB)

We introduce (integro-differential) harmonic maps into spheres, which are defined as critical points of the Besov-Slobodeckij energy Ω Ω|u(x)−u(y)|ps  |x−y|n+spsdxdy. 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.

24.11.2021, 02:16