Sets of finite perimeter associated with vector fields and polyhedral approximation

Francescopaolo Montefalcone

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2003)

  • Volume: 14, Issue: 4, page 279-295
  • ISSN: 1120-6330

Abstract

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Let X = X 1 , ⋯ , X m be a family of bounded Lipschitz continuous vector fields on 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.

How to cite

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Montefalcone, Francescopaolo. "Sets of finite perimeter associated with vector fields and polyhedral approximation." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.4 (2003): 279-295. <http://eudml.org/doc/252332>.

@article{Montefalcone2003,
abstract = {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.},
author = {Montefalcone, Francescopaolo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Carnot-Carathéodory metric; Perimeter; Polyhedra; perimeter; polyhedra},
language = {eng},
month = {12},
number = {4},
pages = {279-295},
publisher = {Accademia Nazionale dei Lincei},
title = {Sets of finite perimeter associated with vector fields and polyhedral approximation},
url = {http://eudml.org/doc/252332},
volume = {14},
year = {2003},
}

TY - JOUR
AU - Montefalcone, Francescopaolo
TI - Sets of finite perimeter associated with vector fields and polyhedral approximation
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/12//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 4
SP - 279
EP - 295
AB - 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.
LA - eng
KW - Carnot-Carathéodory metric; Perimeter; Polyhedra; perimeter; polyhedra
UR - http://eudml.org/doc/252332
ER -

References

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