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

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

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

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topNesi, 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 -

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