A complete characterization of invariant jointly rank-r convex quadratic forms and applications to composite materials
Dipartimento di Matematica, Università di Roma “La
Sapienza”, Italy; email@example.com
Revised: 30 June 2005
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.
Mathematics Subject Classification: 74Q20 / 49K20 / 35J50 / 74E30
Key words: Compensated compactness / rank-r convexity / effective conductivity / quadratic forms.
© EDP Sciences, SMAI, 2007