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Following Morrey [14] we associate to any measurable symmetric $2\times 2$ matrix valued function $A\left(x\right)$ such that $$\frac{{\left|\xi \right|}^2}{K}\le \left(A\left(x\right)\xi ,\xi \right)\le K{\left|\xi \right|}^2\text{a.e.}x\in \mathrm{\Omega },\mathrm{\forall }\xi \in {\mathbb{R}}^2,$$ $\mathrm{\Omega }\in {\mathbb{R}}^2$ and to any $u\in W^{1,2}\left(\mathrm{\Omega }\right)$ another symmetric $2\times 2$ matrix valued function $\mathcal{A}=\mathcal{A}\left(A,u\right)$ with $det\mathcal{A}=1$ and satisfying $$\frac{{\left|\xi \right|}^2}{K}\le \left(\mathcal{A}\left(x\right)\xi ,\xi \right)\le K{\left|\xi \right|}^2\text{a.e.}x\in \mathrm{\Omega },\mathrm{\forall }\xi \in {\mathbb{R}}^2,$$ The crucial property of $\mathcal{A}$ is that $\mathcal{A}\nabla u=A\nabla u$, if $\nabla u\ne 0$. We study the properties of $\mathcal{A}$ as a function of $A$ and $u$. In particular, we show that, if $A{}_b\to {}^{G}A$, $u_b\rightharpoonup u$, $\nabla u\ne 0$ and $div{A}_b\nabla u_b=0$ then $\mathcal{A}(A{}_b,u{}_b)\to {}^G\mathcal{A}(A,u)$.