A nonlinear Liouville theorem for fractional equations in the Heisenberg group

DOI10.1016/j.jmaa.2015.07.050zbMath1332.35374arXiv1504.03122OpenAlexW1869379551MaRDI QIDQ497763

Jinggang Tan, Eleonora Cinti

Publication date: 25 September 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.03122

zbMATH Keywords

Heisenberg groupLiouville theoremfractional sub-Laplacianmoving plane method

Mathematics Subject Classification ID

Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Fractional partial differential equations (35R11) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (9)

Properties of solutions to fractional \(p\)-subLaplace equations on the Heisenberg group ⋮ Nonlocal Harnack inequalities in the Heisenberg group ⋮ Variational framework and Lewy-Stampacchia type estimates for nonlocal operators on Heisenberg group ⋮ A Liouville type theorem to an extension problem relating to the Heisenberg group ⋮ Hölder continuity and boundedness estimates for nonlinear fractional equations in the Heisenberg group ⋮ A Liouville theorem for the semilinear fractional CR covariant equation on the heisenberg group ⋮ Unnamed Item ⋮ Liouville type theorems for nonlinear elliptic equations on extended Grushin manifolds ⋮ A direct method of moving planes to fractional power subLaplace equations on the Heisenberg group

Cites Work

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• An extension problem for the CR fractional Laplacian
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Semi-linear Liouville theorems in the Heisenberg group via vector field methods
• The Yamabe problem on CR manifolds
• Symmetry and related properties via the maximum principle
• Classification of solutions of some nonlinear elliptic equations
• Resolvent of the Laplacian on strictly pseudoconvex domains
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Existence of positive solutions of a semilinear elliptic equation in \(\mathbb{R}_+^n\) with a nonlinear boundary condition
• A non-existence theorem for a semilinear Dirichlet problem involving critical exponent on halfspaces of the Heisenberg group
• Liouville theorems for semilinear equations on the Heisenberg group
• Uniqueness theorems through the method of moving spheres
• Liouville type theorem in the Heisenberg group with general nonlinearity
• Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere
• CR-invariants and the scattering operator for complex manifolds with boundary
• Harnack inequality for fractional sub-Laplacians in Carnot groups
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• Scattering and inverse scattering on ACH manifolds
• The Heat Kernel and Frequency Localized Functions on the Heisenberg Group
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Nonlinear liouville theorems in the heisenberg group vip the moving plane method
• On the method of moving planes and the sliding method
• An Extension Problem Related to the Fractional Laplacian
• CR invariant powers of the sub-Laplacian

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