A geometric inequality in the Heisenberg group and its applications to stable solutions of semilinear problems

Fausto Ferrari, Enrico Valdinoci

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

In the Heisenberg group framework, we obtain a geometric inequality for stable solutions of Δℍ u = f (u) in a domain Ω⊆ℍ. More precisely, if we denote the horizontal intrinsic Hessian by Hu, the mean curvature of a level set by h, its imaginary curvature by p, the intrinsic normal by ν and the unit tangent by υ, we have that Mathematic expression for any Mathematic expression. Stable solutions in the entire ℍ satisfying a suitably weighted energy growth and such that Mathematic expression are then shown to have level sets with vanishing mean curvature.

Original languageEnglish
Pages (from-to)351-370
Number of pages20
JournalMathematische Annalen
Volume343
Issue number2
DOIs
Publication statusPublished - 1 Feb 2009
Externally publishedYes

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