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.

A complete characterization of invariant jointly rank-r convex quadratic forms and applications to composite materials / Nesi, Vincenzo; Rogora, Enrico. - In: ESAIM. COCV. - ISSN 1292-8119. - 13:(2007), pp. 1-34. [10.1051/cocv:2007002]

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

NESI, Vincenzo;ROGORA, Enrico
2007

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.
2007
01 Pubblicazione su rivista::01a Articolo in rivista
A complete characterization of invariant jointly rank-r convex quadratic forms and applications to composite materials / Nesi, Vincenzo; Rogora, Enrico. - In: ESAIM. COCV. - ISSN 1292-8119. - 13:(2007), pp. 1-34. [10.1051/cocv:2007002]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/70675
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