*Accepted Paper*

**Inserted:** 19 jul 2019

**Last Updated:** 29 jan 2021

**Journal:** Journal of Functional Analysis

**Volume:** 278

**Number:** 10

**Year:** 2020

**Doi:** j.jfa.2019.108453

**Abstract:**

Let $\mathcal{N}$ be a smooth, compact, connected Riemannian manifold without boundary. Let $\mathcal{E}\to\mathcal{N}$ be the Riemannian universal covering of $\mathcal{N}$. For any bounded, smooth domain $\Omega\subseteq\mathbb{R}^d$ and any $u\in\mathrm{BV}(\Omega, \, \mathcal{N})$, we show that $u$ has a lifting $v\in\mathrm{BV}(\Omega, \, \mathcal{E})$. Our result proves a conjecture by Bethuel and Chiron.

**Keywords:**
BV, lifting problem