Potentials for $mathcal{A}$-quasiconvexity

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.