2014/01/27 by Armin Schikorra · 2 citations
Mathematics · Physics and Astronomy · #Energy (signal processing) #Harmonic #Harmonic function #Harmonic map #Harmonic mean #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons #SPHERES #math.AP #msc:35B65 #msc:35J60 #msc:35S05 #msc:58E20
paper · pdf · doi:10.1080/03605302.2014.974059
arxiv created 2014/01/27 · openalex publication_date 2014/10/27 · arxiv updated 2015/04/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
For s ∈ (0, 1) we introduce (integro-differential) harmonic maps v: Ω ⊂ ℝn → ℝN, which are defined as critical points of the Gagliardo/Slobodeckij energywith the condition that v(Ω) ⊂ 𝕊N−1, for the (N − 1)-sphere 𝕊N−1 ⊂ ℝN. If p = 2 these are the classical fractional harmonic maps first considered by Da Lio and Rivière. For p ≠ 2 this is a new energy which has degenerate, non-local Euler-Lagrange equations. They are different from the n/p-harmonic maps introduced by Da Lio and the author, and have to be treated with new arguments, which might be of independent interest for further applications on geometric energies. The main result is Hölder continuity for these maps in the critical case .