Regularity of dbar on worm domains

Dariush Ehsani

Regularity of dbar on worm domains

Complex Variables 2014-08-04 v2

Authors: Dariush Ehsani

Abstract

A solution operator to the $\bar{\partial}$ -equation is constructed on unbounded worm domains, $D_{\beta}$ . Regularity estimates are proven showing the operator preserves regularity of the data. The operator may be viewed as a continuous mapping among appropriate subpaces of $W^s(D_{\beta})$ , which depend on a rotational invariance of the domains.

Keywords

$\bar{\partial}$-equation worm domains solution operator regularity estimates unbounded domains rotational invariance Sobolev spaces

Cite

@article{arxiv.1406.7380,
  title  = {Regularity of dbar on worm domains},
  author = {Dariush Ehsani},
  journal= {arXiv preprint arXiv:1406.7380},
  year   = {2014}
}

Comments

Paper is withdrawn due to error in the proof of Lemma 2.1

Related papers

View all related →