Sobolev $\frac{1}{2}$ estimates for $\overline{\partial}$ equations on strictly pseudoconvex domains with $C^2$ boundary

Ziming Shi; Liding Yao

Sobolev $\frac{1}{2}$ estimates for $\overline{\partial}$ equations on strictly pseudoconvex domains with $C^2$ boundary

Complex Variables 2021-07-20 v1 Analysis of PDEs Classical Analysis and ODEs

Authors: Ziming Shi , Liding Yao

Abstract

We construct a solution operator for $\overline{\partial}$ equation that gains $\frac{1}{2}$ derivative in the fractional Sobolev space $H^{s,p}$ on bounded strictly pseudoconvex domains in $\mathbb{C}^n$ with $C^2$ boundary, for all $1 < p < \infty$ and $s > \frac{1}{p}$ .

Keywords

sobolev estimates overline partial equation strictly pseudoconvex domains fractional sobolev spaces c2 boundary

Cite

@article{arxiv.2107.08913,
  title  = {Sobolev $\frac{1}{2}$ estimates for $\overline{\partial}$ equations on strictly pseudoconvex domains with $C^2$ boundary},
  author = {Ziming Shi and Liding Yao},
  journal= {arXiv preprint arXiv:2107.08913},
  year   = {2021}
}

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31 pages

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