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

Vincenzo Nesi; Enrico Rogora

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 1, page 1-34
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Nesi, Vincenzo, and Rogora, Enrico. "A complete characterization of invariant jointly rank-r convex quadratic forms and applications to composite materials." ESAIM: Control, Optimisation and Calculus of Variations 13.1 (2007): 1-34. <http://eudml.org/doc/249995>.

@article{Nesi2007,
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. },
author = {Nesi, Vincenzo, Rogora, Enrico},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Compensated compactness; rank-r convexity; effective conductivity; quadratic forms.; effective conductivity; extremal 2-forms},
language = {eng},
month = {2},
number = {1},
pages = {1-34},
publisher = {EDP Sciences},
title = {A complete characterization of invariant jointly rank-r convex quadratic forms and applications to composite materials},
url = {http://eudml.org/doc/249995},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Nesi, Vincenzo
AU - Rogora, Enrico
TI - A complete characterization of invariant jointly rank-r convex quadratic forms and applications to composite materials
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/2//
PB - EDP Sciences
VL - 13
IS - 1
SP - 1
EP - 34
AB - 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.
LA - eng
KW - Compensated compactness; rank-r convexity; effective conductivity; quadratic forms.; effective conductivity; extremal 2-forms
UR - http://eudml.org/doc/249995
ER -

References

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