Quasiconformal mappings as a tool to study certain two-dimensional \(G\)-closure problems
type: Item
instance of: scholarly article
title: Quasiconformal mappings as a tool to study certain two-dimensional \(G\)-closure problems
zbMATH Open document ID: 0854.30015
DOI: 10.1007/BF00376254
author: V. Nesi
published in: Archive for Rational Mechanics and Analysis
publication date: 1997-01-13T00:00:00Z
review text: A recent theorem due to Astala establishes the best exponent for the area distortion of planar \(K\)-quasiconformal mappings. The author uses a refinement of Astala's theorem due to Eremenko and Hamilton to prove new bounds on the effective conductivity of two-dimensional composites. The bounds are valid for composites made of an arbitrary finite number \(n\) of possibly anisotropic phases in prescribed volume fractions. For \(n = 2\) he proves the optimality of the bounds under certain additional assumptions on the \(G\)-closure parameters.
Mathematics Subject Classification ID: 30C62
Mathematics Subject Classification ID: 35J99
zbMATH DE Number: 909629
zbMATH Keywords: \(K\)-quasiconformal mappings
reviewed by: Jürgen Appell
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00376254
OpenAlex ID: W2073626060
description: scientific article; zbMATH DE number 909629