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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 aquotient of $L^{1}(U;\mathbb{R}^{n})$.

On an identification of the Lipschitz-free spaces over subsets of $\mathbb{R}^{n}$