Extremal rank-one convex integrands and a conjecture of Šverák

Abstract

We show that in order to decide whether a given probability measure is laminate it is enough to verify Jensen's inequality in the class of extremal non-negative rank-one convex integrands. We also identify a subclass of these extremal integrands, consisting of truncated minors, thus proving a conjecture made by Šverák in (Arch. Ration. Mech. Anal. 119 293-300, 1992).