Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
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.