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.

中文翻译：

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两个弱q-凸域的交点上的$$ \ bar {\ partial} $$∂-Neumann问题

我们在两个有界弱q凸域与\（\ mathcal {C} ^ 2 \）的交集上为\（\ bar {\ partial} \）- Neumann运算符\（N_s \）建立一些函数分析性质- \（\ mathbb {C} ^ n \）中的边界。对于所有\（s \ ge q \）来说，注意力集中在\（L ^ 2 \） - \（N_s \）的存在性和紧凑性上。因此实现了\（\ bar {\ partial} \）方程的Sobolev和边界正则性。