  We prove that $W^{1}_{p}$ is an interpolation space between $W^{1}_{p_{1}}$
and $W^{1}_{p_{2}}$ for $p>q_{0}$ and $1\leq p_{1}<p<p_{2}\leq \infty$ on some
classes of manifolds and general metric spaces, where $q_{0}$ depends on our
hypotheses.
