For $l$-homogeneous linear differential operators $\mathcal{A}$ of constant rank, we study the implication $v_j\rightharpoonup v$ in $X$ and $\mathcal{A} v_j\rightarrow \mathcal{A} $W^{-l}Y$ implies $F(v_j)\rightsquigarrow F(v)$ $Z$, where $F$ is an $\mathcal{A}$-quasiaffine function $\rightsquigarrow$ denotes appropriate type weak convergence. Here $Z$ a local $L^1$-type space, either space $\...