Geodesic
Sets of finite perimeter associated with vector fields and polyhedral approximation
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 14 (2003) no. 4, pp. 279-295.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Let $X = X_{1}, \cdots, X_{m}$ be a family of bounded Lipschitz continuous vector fields on $\mathbb{R}^{n}$. In this paper we prove that if $E$ is a set of finite $X$-perimeter then his $X$-perimeter is the limit of the $X$-perimeters of a sequence of euclidean polyhedra approximating $E$ in $L^{1}$-norm. This extends to Carnot-Carathéodory geometry a classical theorem of E. De Giorgi.
Sia data in $\mathbb{R}^{n}$ una m-upla $X = X_{1}, \cdots, X_{m}$ di campi vettoriali lipschitziani e limitati. In questo lavoro dimostriamo che se $E$ è un insieme di $X$-perimetro finito allora l’$X$-perimetro di $E$ è il limite degli $X$-perimetri di una successione di poliedrali euclidee approssimanti $E$ in norma $L^{1}$. Questo risultato estende alle geometrie di tipo Carnot-Carathéodory un classico teorema di E. De Giorgi. 
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Montefalcone, Francescopaolo. Sets of finite perimeter associated with vector fields and polyhedral approximation. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 14 (2003) no. 4, pp. 279-295. http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_4_a1/

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