  In the recent paper \cite{SER}, the second author proved a
divergence-quasiconcavity inequality for the following functional $
\mathbb{D}(A)=\int_{\mathbb{T}^n} det(A(x))^{\frac{1}{n-1}}\,dx$ defined on the
space of $p$-summable positive definite matrices with zero divergence. We prove
that this implies the weak upper semicontinuity of the functional
$\mathbb{D}(\cdot)$ if and only if $p>\frac{n}{n-1}$.
