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. 
@article{RLIN_2003_9_14_4_a1,
     author = {Montefalcone, Francescopaolo},
     title = {Sets of finite perimeter associated with vector fields and polyhedral approximation},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {279--295},
     publisher = {mathdoc},
     volume = {Ser. 9, 14},
     number = {4},
     year = {2003},
     zbl = {1072.49031},
     mrnumber = {MR2104216},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_4_a1/}
}
TY  - JOUR
AU  - Montefalcone, Francescopaolo
TI  - Sets of finite perimeter associated with vector fields and polyhedral approximation
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
PY  - 2003
SP  - 279
EP  - 295
VL  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_4_a1/
LA  - en
ID  - RLIN_2003_9_14_4_a1
ER  - 
%0 Journal Article
%A Montefalcone, Francescopaolo
%T Sets of finite perimeter associated with vector fields and polyhedral approximation
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 2003
%P 279-295
%V 14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_2003_9_14_4_a1/
%G en
%F RLIN_2003_9_14_4_a1
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/