Sets of finite perimeter associated with vector fields and polyhedral approximation

Montefalcone, Francescopaolo

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 14 (2003) no. 4, pp. 279-295

Résumé

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.