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arXiv · 1505.07042

The $\overline{\partial}$-equation on variable strictly pseudoconvex domains

Xianghong Gong·Kang-Tae Kim
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Abstract

We investigate regularity properties of the $\overline{\partial}$-equation on domains in a complex euclidean space that depend on a parameter. Both the interior regularity and the regularity in the parameter are obtained for a continuous family of pseudoconvex domains. The boundary regularity and the regularity in the parameter are also obtained for smoothly bounded strongly pseudoconvex domains.

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Xianghong Gong, Kang-Tae Kim. 2015-05-26. The $\overline{\partial}$-equation on variable strictly pseudoconvex domains. https://arxiv.org/abs/1505.07042

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