  In this short note, we develop a method for identifying the spaces
$Lip_{0}(U)$ for every nonempty open convex $U$ of $\mathbb{R}^{n}$ and
$n\in\mathbb{N}$. Moreover, we show that $\mathcal{F}(U)$ is identified with a
quotient of $L^{1}(U;\mathbb{R}^{n})$.
