Estimating invertible domains of diffeomorphisms
type: Item
instance of: scholarly article
title: Estimating invertible domains of diffeomorphisms
zbMATH Open document ID: 1272.47073
author: Jinhai Chen
published in: Journal of Optimization Theory and Applications
publication date: 2013-02-11T00:00:00Z
review text: In nonlinear analysis, the classical inverse function theorem provides sufficient conditions for a differentiable map to be invertible. However, the theorem only indicates the existence of an invertible neighborhood for the diffeomorphism. The present paper is concerned with estimates on the domain of invertibility for a diffeomorphism in Banach spaces. The results improve the estimates known in the literature (see, for example, [\textit{O. G. Mustafa} and \textit{Yu. V. Rogovchenko}, Proc. Am. Math. Soc. 135, No. 1, 69--75 (2007; Zbl 1116.34004)]). The main tool used in the paper is the continuation property of a diffeomorphism. An application of the obtained results to implicit function theorems is also given.
reviewed by: Elena V. Tabarintseva
Mathematics Subject Classification ID: 47J07
Mathematics Subject Classification ID: 46T20
Mathematics Subject Classification ID: 57R50
zbMATH DE Number: 6135500
zbMATH Keywords: domain of invertibility
zbMATH Keywords: diffeomorphism
zbMATH Keywords: continuation property
zbMATH Keywords: Hadamard-Lévy's condition
MaRDI profile type: Publication
full work available at URL: s10957-012-0063-0
OpenAlex ID: W2016162045
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DOI: 10.1007/S10957-012-0063-0
description: scientific article; zbMATH DE number 6135500