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

Abstract

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