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Univalent σ-harmonic mappings: applications to composites

Published online by Cambridge University Press:  15 September 2002

Giovanni Alessandrini and
Vincenzo Nesi
Giovanni Alessandrini
Affiliation:
Dipartimento di Scienze Matematiche, Universitá degli Studi di Trieste, Via A. Valerio 12/1, 34127 Trieste, Italy; alessang@univ.trieste.it.
Vincenzo Nesi
Affiliation:
Dipartimento di Matematica, Universitá di Roma, La Sapienza, P. le A. Moro 2, 00185 Rome, Italy; nesi@mat.uniroma1.it.
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Abstract

This paper is part of a larger project initiated with [2]. Thefinal aim of the present paper is to give bounds for the homogenized (oreffective) conductivity in two dimensional linear conductivity. The main focus istherefore the periodic setting. We prove new variational principles thatare shown to be of interest in finding bounds on the homogenizedconductivity. Our results unify previous approaches by the second author and maketransparent the central role of quasiconformal mappings in all the two dimensionalG-closure problems in conductivity.

Keywords

Effective propertiesharmonic mappingscomposite materialsquasiregularmappings.

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Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002, pp. 379 - 406
Copyright
© EDP Sciences, SMAI, 2002

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