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

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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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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Xianghong Gong

  2. Department of Mathematics, POSTECH, Pohang, 790-784, Republic of Korea

    Kang-Tae Kim

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  1. Xianghong Gong
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  2. Kang-Tae Kim
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Correspondence to Xianghong Gong.

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Gong, X., Kim, KT. The \(\overline{\partial }\)-equation on variable strictly pseudoconvex domains. Math. Z. 290, 111–144 (2018). https://doi.org/10.1007/s00209-017-2011-z

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  • DOI: https://doi.org/10.1007/s00209-017-2011-z

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