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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]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all the two dimensional G-closure problems in conductivity.

Keywords

Effective propertiesharmonic mappingscomposite materialsquasiregular mappings.
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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