The $\bar{\partial}$-Neumann operator with the Sobolev norm of integer orders

Phillip Harrington; Bingyuan Liu

The $\bar{\partial}$-Neumann operator with the Sobolev norm of integer orders

Complex Variables 2019-05-13 v1 Analysis of PDEs

Authors: Phillip Harrington , Bingyuan Liu

Abstract

Let $\Omega\subset\mathbb{C}^m$ be a bounded pseudoconvex domain with smooth boundary. For each $k\in\mathbb{N}$ , we give a sufficient condition to estimate the $\bar\partial$ -Neumann operator in the Sobolev space $W^k(\Omega)$ . The key feature of our results is a precise formula for $k$ in terms of the geometry of the boundary of $\Omega$ .

Keywords

bounded domains sobolev spaces operator theory

Cite

@article{arxiv.1905.04238,
  title  = {The $\bar{\partial}$-Neumann operator with the Sobolev norm of integer orders},
  author = {Phillip Harrington and Bingyuan Liu},
  journal= {arXiv preprint arXiv:1905.04238},
  year   = {2019}
}

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