Obstructions to the extension problem of Sobolev mappings
type: Item
instance of: scholarly article
title: Obstructions to the extension problem of Sobolev mappings
zbMATH Open document ID: 1035.46045
DOI: 10.12775/TMNA.2003.021
author: Takeshi Isobe
published in: Topological Methods in Nonlinear Analysis
publication date: 2003-10-27T00:00:00Z
review text: Let \(M\) and \(N\) be compact manifolds with \(\partial M \neq \emptyset\). In the present paper, the author shows that when \(1<p <\dim M\), then there are two different obstructions to extending a map in \(W^{1-1/p,p}(\partial M, N)\) to a map in \(W^{1,p}(M,N)\). The author characterizes one of these obstructions which is topological in nature. He also gives properties of the other obstruction. For some cases, he gives a characterization of those \(f\in W^{1-1/p,p}(\partial M,N)\) which have an extension \(F\in W^{1,p}(M,N)\).
Mathematics Subject Classification ID: 46T10
Mathematics Subject Classification ID: 46T30
Mathematics Subject Classification ID: 55P05
Mathematics Subject Classification ID: 55S35
Mathematics Subject Classification ID: 55S36
Mathematics Subject Classification ID: 58D15
zbMATH DE Number: 1997223
zbMATH Keywords: Sobolev mappings
zbMATH Keywords: extension problem
zbMATH Keywords: trace spaces
zbMATH Keywords: obstruction theory.
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
full work available at URL: tmna.2003.021
OpenAlex ID: W2547058372
description: scientific article; zbMATH DE number 1997223