\(\mu(z)\)-homeomorphisms in the plane
type: Item
instance of: scholarly article
title: \(\mu(z)\)-homeomorphisms in the plane
zbMATH Open document ID: 1053.30009
author: Zhiquo Chen
published in: Michigan Mathematical Journal
publication date: 2004-06-15T00:00:00Z
review text: This paper deals with \(\mu(z)\) homeomorphisms of a domain \(\Omega\) of the complex plane, that are topological mappings which are \(ACL\) in \(\Omega\) and satisfy the Beltrami equation \[ f_{\overline{z}}(z) = \mu(z) f_z(z), \;z \in \Omega, \] where \(\mu(z)\) is a measurable function with \(| \mu(z)| <1\). Let \(D(z)= \frac{1+| \mu(z)| }{1-| \mu(z)| }\) the dilatation function, then an existence and a uniqueness theorem is proven under the assumptions that \(D(z)\) is locally in \(L^\lambda (C)\) for some \(\lambda > 1\) and under conditions for the integral mean of \(D(z)\).
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 2075170
zbMATH Keywords: quasiconformal mappings
zbMATH Keywords: Beltrami equation
reviewed by: Bodo Dittmar
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1070919559
OpenAlex ID: W1993150832
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DOI: 10.1307/MMJ/1070919559
description: scientific article; zbMATH DE number 2075170