Lp-gradient harmonic maps into spheres and SO(N)

Armin Schikorra

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Submission date: 15. Mar. 2014
Pages: 29
published in: Differential and integral equations, 28 (2015) 3/4, p. 383-408 
Bibtex
MSC-Numbers: 58E20, 35B65, 35J60
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Abstract:
We consider critical points of the energy E(v) := ∫ _ℝⁿ|∇^sv|, where v maps locally into the sphere or SO(N), and ∇^s = (∂₁^s,…,∂_n^s) is the formal fractional gradient, i.e. ∂_α^s is a composition of the fractional laplacian with the α-th Riesz transform. We show that critical points of this energy are Hölder continuous. As a special case, for s = 1, we obtain a new, more stable proof of Fuchs and Strzelecki’s regularity result of n-harmonic maps into the sphere, which is interesting on its own.