Maximally singular Sobolev functions
type: Item
instance of: scholarly article
title: Maximally singular Sobolev functions
zbMATH Open document ID: 1073.46023
author: Darko Žubrinić
author: Lana Horvat Dmitrović
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-18T00:00:00Z
review text: In any Sobolev space \(W^{m,p}(\mathbb{R}^N)\) with \(p>1\), \(mp\leq N\), a function is constructed, the set of singular points of which has the maximal possible Hausdorff dimension equal to \(N-mp\). The analogous result is proven also for Bessel potential spaces \(L^{\alpha,p}(\mathbb{R})\) with \(\alpha>0\), \(p>1\).
reviewed by: Giorgi Oniani
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 2157698
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: Bessel potential space
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: singular point
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.09.047
OpenAlex ID: W2081480280
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DOI: 10.1016/J.JMAA.2004.09.047
description: scientific article; zbMATH DE number 2157698