The polynomial growth solutions to some sub-elliptic equations on the Heisenberg group

DOI10.1142/S0219199717500699zbMath1406.35452OpenAlexW2745535772MaRDI QIDQ4622585

Tian Long, Xiao-Ping Yang, Hai-Rong Liu

Publication date: 13 February 2019

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199717500699

zbMATH Keywords

Heisenberg grouppolynomial growth solutionsub-elliptic equations\(H\)-periodicity

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (1)

Critical points of solutions of sub-elliptic equations on the Heisenberg group

Cites Work

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• Properties of a frequency of Almgren type for harmonic functions in Carnot groups
• Balls and metrics defined by vector fields. I: Basic properties
• Fundamental solutions and geometry of the sum of squares of vector fields
• Hypoelliptic differential operators and nilpotent groups
• Harmonic functions on manifolds
• Two-scale homogenization in the Heisenberg group
• Counting massive sets and dimensions of harmonic functions.
• Exponential growth solutions of elliptic equations
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Counting dimensions of \(L\)-harmonic functions
• The growth of \(H\)-harmonic functions on the Heisenberg group
• Hypoelliptic second order differential equations
• Polynomial growth solutions of uniformly elliptic operators of non-divergence form
• Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Sobolev met Poincaré
• On a Liouville-type theorem for linear and nonlinear elliptic differential equations on a torus
• Homogenization and Convergence of Correctors in Carnot Groups
• Integral representations and Liouville theorems for solutions of periodic elliptic equations

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