Transformations that preserve Sobolev spaces
type: Item
instance of: scholarly article
title: Transformations that preserve Sobolev spaces
zbMATH Open document ID: 0588.30025
DOI: 10.1007/BF00968977
author: V. M. Gol'dshtejn
author: A. S. Romanov
published in: Siberian Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: The following theorem is proved: If the mapping \(\phi\) : \(G\to G'\) between the domains G and G' in \({\mathbb{R}}^ n\) induces an isomorphism \(\phi^*: W^ 1_ p(G')\to W^ 1_ p(G)\) between the Sobolev-spaces with index p where \(p\in (n-1,n)\) then \(\phi\) coincides a.e. with a quasi-isometry.
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 3944222
zbMATH Keywords: quasi-isometry
MaRDI profile type: Publication
cites work: Quasiconformal Mappings and Royden Algebras in Space
cites work: Q5597806
full work available at URL: https://doi.org/10.1007/bf00968977
OpenAlex ID: W2038194250
description: scientific article; zbMATH DE number 3944222