Injective mappings and solvable vector fields of Euclidean spaces.
type: Item
instance of: scholarly article
title: Injective mappings and solvable vector fields of Euclidean spaces.
zbMATH Open document ID: 1037.57023
author: D. Massart
published in: Topology and its Applications
publication date: 2004-02-03T00:00:00Z
review text: Let \(\Omega\) be an open connected subset of \(\mathbb{R}^n\) and let \(\Phi(\Omega)\) denote the subset of \(C^\infty(\Omega,\mathbb{R}^n)\) consisting of the mappings \(F\) having invertible derivative \(F'(x)\) for each \(x\in\Omega\). Under a generalized convexity condition, the injectivity of a mapping \(F\in \Phi(\Omega)\) for \(n=2\) and \(3\) is proved. Connections with global solvability of partial differential equations are discussed.
Mathematics Subject Classification ID: 57R35
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 57R25
zbMATH DE Number: 2037258
zbMATH Keywords: global injectivity
zbMATH Keywords: charateristics and global solvability of partial differential equations
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
full work available at URL: j.topol.2003.05.001
OpenAlex ID: W2049275445
Wikidata QID: Q114128113
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DOI: 10.1016/J.TOPOL.2003.05.001
description: scientific article; zbMATH DE number 2037258