The $$\bar{\partial }$$-Neumann problem on the intersection of two weakly q-convex domains

Abstract

We establish some functional analytic properties for the $$\bar{\partial }$$ -Neumann operator $$N_s$$ on the intersection of two bounded weakly q-convex domains with $$\mathcal {C}^2$$ -boundaries in $$\mathbb {C}^n$$ . Attention is focussed on questions of $$L^2$$ -existence and compactness of $$N_s$$ for all $$s\ge q$$ . Sobolev and boundary regularity for the $$\bar{\partial }$$ -equation are consequently achieved.