English

Exact sequences and estimates for the $\overline{\partial}$-problem

Complex Variables 2020-07-14 v1

Abstract

We study Sobolev estimates for solutions of the inhomogenous Cauchy-Riemann equations on annuli in \cxn\cx^n, by constructing exact sequences relating the Dolbeault cohomology of the annulus with respect to Sobolev spaces of forms with those of the envelope and the hole. We also obtain solutions with prescibed support and estimates in Sobolev spaces using our method.

Keywords

Cite

@article{arxiv.2007.06405,
  title  = {Exact sequences and estimates for the $\overline{\partial}$-problem},
  author = {Debraj Chakrabarti and Phil Harrington},
  journal= {arXiv preprint arXiv:2007.06405},
  year   = {2020}
}
R2 v1 2026-06-23T17:04:40.326Z