# Solutions of the fractional Allen-Cahn equation which are invariant under screw motion

created by cinti on 02 Sep 2015
modified on 27 Jul 2016

[BibTeX]

Accepted Paper

Inserted: 2 sep 2015
Last Updated: 27 jul 2016

Journal: J. London Math. Soc.
Year: 2015

Abstract:

We establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in $\mathbb R^3$, which vanish on helicoids and are invariant under screw-motion. In addition, we prove that helicoids are surfaces with vanishing nonlocal mean curvature.