To the problem of determining a mapping from its normalized Jacobi matrix

For a mapping $f\colon D\to\mathbb{R}^n$, where $D$ is a domain in $\mathbb{R}^n$, the problem of determining the mapping from its normalized Jacobi matrix $K(x)=|J(x,f)|^{-1/n}f'(x)$ is studied, where $J(x,f)$ is the Jacobian of $f$. It is proved that the necessary condition on $K(x)$ established by the author earlier in the case of mappings of class $C^3$ remain valid for a more general class of mappings with bounded mean distortion. Also, an existence theorem is proved and a formula is presented which enables us to recover the mapping from its normalized Jacobi matrix. A connection between the indicated problem and the known theorems on overdetermined systems is discussed.