Balls defined by nonsmooth vector fields and the Poincaré inequality
Annales de l'Institut Fourier, Volume 54 (2004) no. 2, p. 431-452
We provide a structure theorem for Carnot-Carathéodory balls defined by a family of Lipschitz continuous vector fields. From this result a proof of Poincaré inequality follows.
On prouve un théorème de structure pour les boules de Carnot-Carathéodory définies par des champs de vecteurs lipschitziens. Une inégalité de Poincaré est aussi démontrée.
DOI : https://doi.org/10.5802/aif.2024
Classification:  46E35
Keywords: vector fields, Carnot-Carathéodory distance, Poincaré inequality
@article{AIF_2004__54_2_431_0,
     author = {Montanari, Annamaria and Morbidelli, Daniele},
     title = {Balls defined by nonsmooth vector fields and the Poincar\'e inequality},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {2},
     year = {2004},
     pages = {431-452},
     doi = {10.5802/aif.2024},
     zbl = {1069.46504},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_2_431_0}
}
Montanari, Annamaria; Morbidelli, Daniele. Balls defined by nonsmooth vector fields and the Poincaré inequality. Annales de l'Institut Fourier, Volume 54 (2004) no. 2, pp. 431-452. doi : 10.5802/aif.2024. http://www.numdam.org/item/AIF_2004__54_2_431_0/

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