n/p-harmonic maps: regularity for the sphere case
Francesca Da Lio and Armin Schikorra
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Submission date: 17. Jul. 2012
published in: Advances in calculus of variations, 7 (2014) 1, p. 1-26
DOI number (of the published article): 10.1515/acv-2012-0107
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We introduce n/p-harmonic maps as critical points of the energy E(v) = ∫ |Δα∕2v|p where pointwise v : D ⊂ ℝn → SN-1, for the N-sphere SN-1 ⊂ ℝN and α = n∕p. This energy combines the non-local behaviour of the fractional harmonic maps introduced by Riviere and first author with the degenerate arguments of the n-laplacian. In this setting, we will prove Hölder continuity.