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.

A geometric inequality in the Heisenberg group and its applications to stable solutions of semilinear problems / F. Ferrari, E. Valdinoci. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 343:2(2009), pp. 351-370.

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

E. Valdinoci
Primo
2009

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.
Settore MAT/05 - Analisi Matematica
2009
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/266022
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