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A complete characterization of invariant jointly rank-r convex quadratic forms and applications to composite materials

Published online by Cambridge University Press:  14 February 2007

Vincenzo Nesi  and
Enrico Rogora
Vincenzo Nesi
Affiliation:
Dipartimento di Matematica, Università di Roma “La Sapienza”, Italy;  nesi@mat.uniroma1.it
Enrico Rogora
Affiliation:
Dipartimento di Matematica, Università di Roma “La Sapienza”, Italy;  nesi@mat.uniroma1.it
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Abstract

The theory of compensated compactness of Murat and Tartar links the algebraic condition of rank-r convexity with the analytic condition of weak lower semicontinuity. The former is an algebraic condition and therefore it is, in principle, very easy to use. However, in applications of this theory, the need for an efficient classification of rank-r convex forms arises. In the present paper, we define the concept of extremal 2-forms  and characterize them in the rotationally invariant jointly rank-r convex case.

Keywords

Compensated compactnessrank-r convexityeffective conductivityquadratic forms.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 1 , January 2007 , pp. 1 - 34
Copyright
© EDP Sciences, SMAI, 2007

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