Weak differentiability of BV functions on stratified groups
type: Item
instance of: scholarly article
title: Weak differentiability of BV functions on stratified groups
zbMATH Open document ID: 1048.49030
author: Valentino Magnani
author: Luigi Ambrosio
published in: Mathematische Zeitschrift
publication date: 2003-12-16T00:00:00Z
review text: Given a simply connected stratified nilpotent Lie group \(\mathbb{G}\) and an open subset \(\Omega\) of \(\mathbb{G}\), the authors introduce a natural concept for functions \(u\in L^1(\Omega)\) to be of bounded variation extending the definition known for the Euclidean case. They then prove the almost everywhere approximate differentiability of these functions and study the size of their approximate discontinuity sets. In further sections they discuss functions of bounded higher order variation and present a weak version of Alexandroff's differentiability theorem.
Mathematics Subject Classification ID: 49Q15
zbMATH DE Number: 2018248
zbMATH Keywords: functions in stratified groups
zbMATH Keywords: approximate differentiability
zbMATH Keywords: functions of bounded higher order variation
reviewed by: M. Fuchs
MaRDI profile type: Publication
full work available at URL: s00209-003-0530-2
OpenAlex ID: W2084707445
Wikidata QID: Q125856181
DOI: 10.1007/S00209-003-0530-2
description: scientific article; zbMATH DE number 2018248