Anisotropic surface measures as limits of volume fractions
type: Item
instance of: scholarly article
title: Anisotropic surface measures as limits of volume fractions
zbMATH Open document ID: 1408.49008
DOI: 10.1007/978-3-319-89800-1_1
author: Luigi Ambrosio
author: Giovanni E. Comi
publication date: 2019-01-24T00:00:00Z
review text: The new characterization of the perimeter of a measurable set in \(\mathbb R^n\) due to [the first author et al., Commun. Pure Appl. Math. 69, No. 6, 1062--1086 (2016; Zbl 1352.46026)] is considered in the paper. Their approach is modified by using covering families made by translations of a given open bounded set with Lipschitz boundary. The main result is Theorem 1 formulated in the Introduction. It is proved in Section 3 by a simple comparison argument based on the results of [loc. cit.]. The proof is technical and interesting. Few examples on coverings and estimates are given in Section 4. For the entire collection see [Zbl 1403.46004].
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 7006518
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: lower and upper density
zbMATH Keywords: isotropic coverings
reviewed by: Stepan Agop Tersian
MaRDI profile type: Publication
full work available at URL: 978-3-319-89800-1 1
OpenAlex ID: W2809512086
description: scientific article; zbMATH DE number 7006518