  Consider the Langevin process, described by a vector (positions and momenta)
in $\mathbb{R}^{d}\times\mathbb{R}^d$. Let $\mathcal O$ be a $\mathcal{C}^2$
open bounded and connected set of $\mathbb{R}^d$. Recent works showed the
existence of a unique quasi-stationary distribution (QSD) of the Langevin
process on the domain $D:=\mathcal{O}\times\mathbb{R}^d$. In this article, we
study the overdamped limit of this QSD, i.e. when the friction coefficient goes
to infinity. In particular, we show that the marginal law in position of the
overdamped limit is the QSD of the overdamped Langevin process on the domain
$\mathcal{O}$.
