Balls defined by nonsmooth vector fields and the Poincaré inequality
[Boules définies par des champs de vecteurs non réguliers et l'inégalité de Poincaré]
Montanari, Annamaria1 ; Morbidelli, Daniele
1 Università di Bologna, Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127 Bologna (Italie)
Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 431-452.

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.

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.

DOI : 10.5802/aif.2024
Classification : 46E35
Keywords: vector fields, Carnot-Carathéodory distance, Poincaré inequality
Mot clés : champs de vecteurs, distance de Carnot-Carathéodory, inégalité de Poincaré
Montanari, Annamaria 1 ; Morbidelli, Daniele 

1 Università di Bologna, Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40127 Bologna (Italie) 
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Montanari, Annamaria; Morbidelli, Daniele. Balls defined by nonsmooth vector fields and the Poincaré inequality. Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 431-452. doi : 10.5802/aif.2024. http://www.numdam.org/articles/10.5802/aif.2024/

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