Isometric representation of Lipschitz-free spaces over convex domains in finite-dimensional spaces

Abstract

Let $E$ be a finite-dimensional normed space and $\Omega$ a nonempty convex open set in $E$. We show that the Lipschitz-free space of $\Omega$ is canonically isometric to the quotient of $L^1(\Omega,E)$ by the subspace consisting of vector fields with zero divergence in the sense of distributions on $E$.