Let $m,n\in\mathbb N$, let $\Omega\subset \mathbb R^n$ be a bounded [open set](/page/Open%20Set), let $1\le r\le \min\{m,n\}$, and let $p\ge r$. Let $u_k,u\in W^{1,p}(\Omega;\mathbb R^m)$ for $k\in\mathbb N$, and suppose that
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\begin{align*}
u_k \rightharpoonup u \quad \text{in } W^{1,p}(\Omega;\mathbb R^m).
\end{align*}
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Write $Ju_k,Ju\in L^p(\Omega;\mathbb R^{m\times n})$ for the weak Jacobian matrices, represented a.e. by
For every strictly increasing row index tuple $I=(i_1,\dots,i_r)$ with $1\le i_1<\cdots<i_r\le m$ and every strictly increasing column index tuple $J=(j_1,\dots,j_r)$ with $1\le j_1<\cdots<j_r\le n$, let $M_{I,J}:\mathbb R^{m\times n}\to\mathbb R$ be the minor map defined by