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MiS Preprint
43/2012
n/p-harmonic maps: regularity for the sphere case
Francesca Da Lio and Armin Schikorra
Abstract
We introduce $n$/$p$-harmonic maps as critical points of the energy $E(v) = \int | \Delta^{\alpha/2} v |^{p}$ where pointwise $v: D \subset \mathbb{R}^n \to \mathbb{S}^{N-1}$, for the $N$-sphere $\mathbb{S}^{N-1} \subset \mathbb{R}^N$ and $\alpha = n/p$. 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.
