Hölder continuous Sobolev mappings and the Lusin N property
type: Item
instance of: scholarly article
title: Hölder continuous Sobolev mappings and the Lusin N property
zbMATH Open document ID: 1331.26021
author: Aleksandra Zapadinskaya
published in: Illinois Journal of Mathematics
publication date: 2015-08-25T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1436275500
review text: Let \(|\cdot |\) and \({\mathcal H}^n\) denote, respectively, the \(n\)-dimensional Lebesgue measure and the \(n\)-dimensional Hausdorff measure. The author gives a new proof of the following theorem: Let \(\Omega\) be a domain in \({\mathbb{R}}^n\) and \(f\in W^{1,n}({\mathbb{R}}^m)\), \(m\geq n\geq 2\), a Hölder continuous mapping. Then, \({\mathcal H}^n (f(E))=0\) for each \(E\subset \Omega\), such that \(|E|=0\). This result was obtained by \textit{J. Malý} and \textit{O. Martio} [J. Reine Angew. Math. 458, 19--36 (1995; Zbl 0812.30007)] for \(n=m\). Then, she generalizes this theorem to a metric setting.
reviewed by: Andrzej Nowak
Mathematics Subject Classification ID: 26B35
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 6475315
zbMATH Keywords: Hölder continuity
zbMATH Keywords: Sobolev mapping
zbMATH Keywords: Lebesgue measure
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: Ahlfors regularity
zbMATH Keywords: Poincaré inequality
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6475315