Basic properties of nonsmooth Hörmander's vector fields and Poincaré's inequality

DOI10.1515/form.2011.133zbMath1357.46027arXiv0809.2872OpenAlexW2108121102MaRDI QIDQ2844271

Marco Pedroni, Marco Bramanti, Luca Brandolini

Publication date: 28 August 2013

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.2872

zbMATH Keywords

Poincaré inequalitynonsmooth Hörmander's vector fields

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) General theory of partial differential operators (47F05) Elliptic equations on manifolds, general theory (58J05) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (15)

Convex hull property and exclosure theorems for \(H\)-minimal hypersurfaces in Carnot groups ⋮ Surface measure on, and the local geometry of, sub-Riemannian manifolds ⋮ Local real analysis in locally homogeneous spaces ⋮ Fundamental solutions and local solvability for nonsmooth Hörmander’s operators ⋮ Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields ⋮ Nonsmooth Hörmander vector fields and their control balls ⋮ A compactness result for BV functions in metric spaces ⋮ The Poincaré inequality for \(C^{1,\alpha}\)-smooth vector fields ⋮ An extension of Hörmander's hypoellipticity theorem ⋮ Multi-parameter Carnot-Carathéodory balls and the theorem of Frobenius ⋮ Poincaré-type inequality for Lipschitz continuous vector fields ⋮ Local Solvability of Nonsmooth Hörmander’s Operators ⋮ The Role of Fundamental Solution in Potential and Regularity Theory for Subelliptic PDE ⋮ On the regularity of vector fields underlying a degenerate-elliptic PDE ⋮ Integral representations for bracket-generating multi-flows

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Commutators of flow maps of nonsmooth vector fields
• Balls and metrics defined by vector fields. I: Basic properties
• Fundamental solutions and geometry of the sum of squares of vector fields
• Fundamental solutions for second order subelliptic operators
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Hypoelliptic differential operators and nilpotent groups
• Free systems of vector fields
• Sobolev and isoperimetric inequalities for degenerate metrics
• \(C^{\infty }\) regularity of solutions of an equation of Levi's type in \(\mathbb{R}^{2n+1}\)
• On the Poincaré inequality for vector fields
• Sobolev and Morrey estimates for non-smooth vector fields of step two
• Smoothness of Lipschitz-continuous graphs with nonvanishing Levi curvature
• The Levi Monge-Ampère equation: smooth regularity of strictly Levi convex solutions
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Pseudoconvex fully nonlinear partial differential operators: strong comparison theorems
• Balls defined by nonsmooth vector fields and the Poincaré inequality.
• The geometric Sobolev embedding for vector fields and the isoperimetric inequality
• Singular and maximal Radon transforms: Analysis and geometry
• Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications
• Hypoelliptic second order differential equations
• Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung
• Regularity properties of solutions of a class of elliptic-parabolic nonlinear Levi type equations
• An embedding theorem for sobolev spaces related to non-smooth vector fieldsand harnack inequality
• Weighted Sobolev-Poincare Inequalities and Pointwise Estimates for a Class of Degenerate Elliptic Equations
• Weighted sobolev-poincaré inequalities for grushin type operators
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]

This page was built for publication: Basic properties of nonsmooth Hörmander's vector fields and Poincaré's inequality