  Assume that $\Omega_{1}$ and $\Omega_{2}$ are two smooth bounded pseudoconvex
domains in $\mathbb{C}^{2}$ that intersect (real) transversely, and that
$\Omega_{1} \cap \Omega_{2}$ is a domain (i.e. is connected). If the
$\overline{\partial}$-Neumann operators on $\Omega_{1}$ and on $\Omega_{2}$ are
compact, then so is the $\overline{\partial}$-Neumann operator on $\Omega_{1}
\cap \Omega_{2}$. The corresponding result holds for the
$\overline{\partial}$-Neumann operators on $(0,n-1)$-forms on domains in
$\mathbb{C}^{n}$.
