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.
Keywords: vector fields, Carnot-Carathéodory distance, Poincaré inequality
Mot clés : champs de vecteurs, distance de Carnot-Carathéodory, inégalité de Poincaré
@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}, pages = {431--452}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {2}, year = {2004}, doi = {10.5802/aif.2024}, zbl = {1069.46504}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2024/} }
TY - JOUR AU - Montanari, Annamaria AU - Morbidelli, Daniele TI - Balls defined by nonsmooth vector fields and the Poincaré inequality JO - Annales de l'Institut Fourier PY - 2004 SP - 431 EP - 452 VL - 54 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2024/ DO - 10.5802/aif.2024 LA - en ID - AIF_2004__54_2_431_0 ER -
%0 Journal Article %A Montanari, Annamaria %A Morbidelli, Daniele %T Balls defined by nonsmooth vector fields and the Poincaré inequality %J Annales de l'Institut Fourier %D 2004 %P 431-452 %V 54 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2024/ %R 10.5802/aif.2024 %G en %F 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://archive.numdam.org/articles/10.5802/aif.2024/
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