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arXiv · 1202.1151

n/p-Harmonic maps: regularity for the sphere case

Francesca Da Lio·Armin Schikorra
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Abstract

We introduce n/p-harmonic maps as critical points of E(v) the Lp-Norm of the alpha-laplacian of v, where pointwise v maps Rn into a sphere, and alpha = n/p. This energy combines the non-local behaviour of the fractional harmonic maps introduced by Riviere and the first author with the degenerate arguments of the n-laplacian. In this setting, we will prove Holder continuity.

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Francesca Da Lio, Armin Schikorra. 2012-02-06. n/p-Harmonic maps: regularity for the sphere case. https://doi.org/10.1515/acv-2012-0107

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