The ∂-equation on variable strictly pseudoconvex domains

2015/05/26 by Gong, Xianghong, Kim, Kang-Tae
#32F15 #32F26 #32W05 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.07042

Abstract

We investigate regularity properties of the ∂-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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