Rigidity results for non local phase transitions in the Heisenberg group $H$

Abstract

In the Heisenberg group framework, we study rigidity properties for stable solutions of $(-{\Delta }_H{)}^{s}v=f(v)$ in $H$, $s\in (0,1)$. We obtain a Poincaré type inequality in connection with a degenerate elliptic equation in ${\mathbb{R}}_{+}^4$; through an extension (or "lifting") procedure, this inequality will be then used for giving a criterion under which the level sets of the above solutions are minimal surfaces in $H$, i.e. they have vanishing mean curvature.

Accepted in Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 2013. v2 quits some unnecessary properties and definitions. arXiv admin note: text overlap with arXiv:1206.0885 by other authors

References in corpus (1)

• The Hessian of the distance from a surface in the Heisenberg group

Cited by in corpus (1)

• An extension problem for the CR fractional Laplacian