Balls defined by nonsmooth vector fields and the Poincaré inequality.

DOI10.5802/aif.2024zbMath1069.46504OpenAlexW2327937602MaRDI QIDQ1890162

Daniele Morbidelli, Annamaria Montanari

Publication date: 20 December 2004

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2004__54_2_431_0

zbMATH Keywords

Poincaré inequalityvector fieldsCarnot-Carathéodory distance

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Invariant metrics and pseudodistances in several complex variables (32F45) Harmonic analysis in several variables (42B99)

Related Items (11)

Step-\(s\) involutive families of vector fields, their orbits and the Poincaré inequality ⋮ GOH Conditions for Minima of Nonsmooth Problems with Unbounded Controls ⋮ Metric geometry of nonregular weighted Carnot-Carathéodory spaces ⋮ Nonsmooth Hörmander vector fields and their control balls ⋮ Attractors met \(X\)-elliptic operators ⋮ An extension of Hörmander's hypoellipticity theorem ⋮ Green function for \(X\)-elliptic operators ⋮ A note on the Poincaré inequality for Lipschitz vector fields of step two ⋮ Poincaré-type inequality for Lipschitz continuous vector fields ⋮ Basic properties of nonsmooth Hörmander's vector fields and Poincaré's inequality ⋮ On the regularity of vector fields underlying a degenerate-elliptic PDE

Cites Work

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• Balls and metrics defined by vector fields. I: Basic properties
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• 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 Poincaré inequality for vector fields satisfying Hörmander's condition
• Analysis on geodesic balls of sub-elliptic operators
• Sobolev met Poincaré
• Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]
• Strong solutions for the Levi curvature equation.

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