The {\bar{\partial}} -Neumann problem on product domains in {\mathbb{C}^{n}} |
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Authors: | Dariush Ehsani |
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Institution: | 1. Department of Mathematics, Penn State, Lehigh Valley, Fogelsville, PA, 18051, USA
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Abstract: | Let ${\Omega=\Omega_{1}\times\cdots\times\Omega_{n}\subset\mathbb{C}^{n}}$ , where ${\Omega_{j}\subset\mathbb{C}}$ is a bounded domain with smooth boundary. We study the solution operator to the ${\overline\partial}$ -Neumann problem for (0,1)-forms on Ω. In particular, we construct singular functions which describe the singular behavior of the solution. As a corollary our results carry over to the ${\overline\partial}$ -Neumann problem for (0,q)-forms. Despite the singularities, we show that the canonical solution to the ${\overline\partial}$ -equation, obtained from the Neumann operator, does not exhibit singularities when given smooth data. |
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