Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T03:05:14.110Z Has data issue: false hasContentIssue false
  • English
  • Français

Strong approximation of sets in BV(Ω)

Published online by Cambridge University Press:  12 November 2008

Thierry Quentin de Gromard
Thierry Quentin de Gromard
Affiliation:
Mathématique, Université Paris Sud, Bâtiment 425, 91405 Orsay Cedex, France ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Taking the argument used by De Giorgi to obtain the rectifiability of the reduced boundary of a set of finite perimeter in ℝN, we prove that a set E of finite perimeter in an open set Ω of ℝN may be approached, in the sense of the BV(Ω) norm, by sets whose boundary is included in a finite union of 1 hypersurfaces; more precisely, arbitrarily large parts (for the N−1 measure in Ω) of the essential boundaries of E and of the approximating set coincide and are included in a single 1 hypersurface.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 6 , December 2008 , pp. 1291 - 1312
Copyright
Copyright © Royal Society of Edinburgh 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)