Traces of Sobolev functions on fractal type sets and characterization of extension domains
type: Item
instance of: scholarly article
title: Traces of Sobolev functions on fractal type sets and characterization of extension domains
zbMATH Open document ID: 0877.46025
author: Piotr Hajłasz
author: O. Martio
published in: Journal of Functional Analysis
publication date: 1997-12-08T00:00:00Z
review text: The authors describe traces of Sobolev functions \(u\in W^{1,p}(\mathbb{R}^n)\), \(1<p\leq\infty\), on certain subsets of \(\mathbb{R}^n\) in terms of Sobolev spaces on metric spaces [see \textit{P. Hajłasz}, Potential Anal. 5, No. 4, 403-415 (1996; Zbl 0859.46022)]. Their results apply to smooth submanifolds, fractal subsets, as well to open subsets of \(\mathbb{R}^n\). In particular if \(\Omega\subset\mathbb{R}^n\) is a John domain, then the authors characterize those \(W^{1,p}(\Omega)\) functions which can be extended to \(W^{1,p}(\mathbb{R}^n)\). In the case of traces on fractal subsets their results are related to those of \textit{A. Jonsson} and \textit{H. Wallin}, ``Function spaces on subsets of \(\mathbb{R}^n\)'' (1984).
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 997641
zbMATH Keywords: traces of Sobolev functions
zbMATH Keywords: smooth submanifolds
zbMATH Keywords: fractal subsets
zbMATH Keywords: John domain
reviewed by: Stanisław Wedrychowicz
MaRDI profile type: Publication
OpenAlex ID: W1993558108
DOI: 10.1006/JFAN.1996.2959
description: scientific article; zbMATH DE number 997641