English

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

Complex Variables 2017-11-15 v2

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.

Keywords

Cite

@article{arxiv.1505.07042,
  title  = {The $\overline{\partial}$-equation on variable strictly pseudoconvex domains},
  author = {Xianghong Gong and Kang-Tae Kim},
  journal= {arXiv preprint arXiv:1505.07042},
  year   = {2017}
}

Comments

Minor revision. To appear in Mathematische Zeitschrift

R2 v1 2026-06-22T09:41:45.341Z