Compactness of the $\bar{\mathrm{\partial }}$-Neumann operator on the intersection of two domains

Assume that ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$ are two smooth bounded pseudoconvex domains in ${\mathbb{C}}^2$ that intersect (real) transversely, and that ${\mathrm{\Omega }}_1\cap {\mathrm{\Omega }}_2$ is a domain (i.e. is connected). If the $\bar{\mathrm{\partial }}$-Neumann operators on ${\mathrm{\Omega }}_1$ and on ${\mathrm{\Omega }}_2$ are compact, then so is the $\bar{\mathrm{\partial }}$-Neumann operator on $\Omega_{1} \cap \Omega_{2}$\mathrm{.}Thecorrespondingresultholdsforthe$\overline{\partial}$-Neumannoperatorson$(0,n-1)$-formsondomainsin$$\mathbb{C}$^{n}$.