Characterization of generalized Young measures generated by $\mathcal A$-free measures

Understand

We give two characterizations, one for the class of generalized Young measures generated by $\mathcal A$-free measures, and one for the class generated by $\mathcal B$-gradient measures $\mathcal Bu$.

• Here, $\mathcal A$ and $\mathcal B$ are linear homogeneous operators of arbitrary order, which we assume satisfy the constant rank property.
• The characterization places the class of generalized $\mathcal A$-free Young measures in duality with the class of $\mathcal A$-quasiconvex integrands by means of a well-known Hahn--Banach separation property.
• A similar statement holds for generalized $\mathcal B$-gradient Young measures.