  We investigate properties of function spaces induced by the inner product
Sobolev spaces $H^{s}(\Omega)$ over a bounded Euclidean domain $\Omega$ and by
an elliptic differential operator $A$ on $\overline{\Omega}$. The domain and
the coefficients of $A$ are of the class $C^{\infty}$. These spaces consist of
all distributions $u\in H^{s}(\Omega)$ such that $Au\in H^{\lambda}(\Omega)$
and are endowed with the corresponding graph norm, with
$s,\lambda\in\mathbb{R}$. We prove an interpolation formula for these spaces
and discuss their application to elliptic boundary-value problems.
