Potentials for $\mathcal{A}$-quasiconvexity

Abstract

We show that each constant rank operator $\mathcal{A}$ admits an exact potential $\mathbb{B}$ in frequency space. We use this fact to show that the notion of $\mathcal{A}$-quasiconvexity can be tested against compactly supported fields. We also show that $\mathcal{A}$-free Young measures are generated by sequences $\mathbb{B}u_j$, modulo shifts by the barycentre.