Semi-linear Liouville theorems in the Heisenberg group via vector field methods

DOI10.1016/J.JDE.2009.08.004zbMath1179.35335OpenAlexW2096228727MaRDI QIDQ1038499

Lu Xu

Publication date: 18 November 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.08.004

zbMATH Keywords

Heisenberg groupvector fieldLiouville theorem

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Semilinear elliptic equations (35J61) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (10)

A Liouville-type theorem for fully nonlinear CR invariant equations on the Heisenberg group ⋮ Liouville theorems to semi-linear degenerate elliptic equation of generalized Baouendi-Grushin vector fields ⋮ Semi-linear Liouville theorems in the generalized Greiner vector fields ⋮ Liouville type results of curvature operators of Fuchsian convex surfaces ⋮ A Liouville theorem for a class semilinear elliptic equations on the Heisenberg group ⋮ On singular solutions of Lane-Emden equation on the Heisenberg group ⋮ Liouville theorems for semilinear differential inequalities on sub-Riemannian manifolds ⋮ Liouville-type results for elliptic equations with advection and potential terms on the Heisenberg group ⋮ A nonlinear Liouville theorem for fractional equations in the Heisenberg group ⋮ A Liouville theorem for superlinear parabolic equations on the Heisenberg group

Cites Work

• Unnamed Item
• The Yamabe problem on CR manifolds
• Classification of solutions of some nonlinear elliptic equations
• Liouville theorems for semilinear equations on the Heisenberg group
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
• The conjectures on conformal transformations of Riemannian manifolds
• Extremals for the Sobolev Inequality on the Heisenberg Group and the CR Yamabe Problem
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Nonlinear liouville theorems in the heisenberg group vip the moving plane method

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