  Given a bounded domain $\Omega \subset \mathbb{R}^n$, a result by Bourgain,
Brezis, and Mironescu characterizes when a function $f \in L^p(\Omega)$ is in
the Sobolev space $W^{1,p}(\Omega)$ based on the limiting behavior of its Besov
seminorms. We prove a direct analogue of this result which characterizes when a
differential $k$-form $\omega \in L^p(\wedge^k T^* \Omega)$ has a weak exterior
derivative $d\omega \in L^p(\wedge^{k+1} T^* \Omega)$, where the analogue of
the Besov seminorm that our result uses is based on integration over simplices.
