Subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces with isolated singularities

Dariush Ehsani

Subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces with isolated singularities

Complex Variables 2022-02-23 v1

Authors: Dariush Ehsani

Abstract

We obtain subelliptic estimates for the $\bar{\partial}$ -problem on complex algebraic surfaces embedded in $\mathbb{C}^n$ with isolated singularities. $W^{\epsilon}$ Sobolev norms of a form, $f$ , for $0< \epsilon < 1$ are estimated in terms of weighted $L^2$ norms of $\bar{\partial} f$ and $\bar{\partial}^{\ast}f$ , with weights which vanish at the singularities, as well as weighted $L^2$ norms of $f$ , with weights which blow up at the singularities.

Keywords

sobolev spaces gradient estimates sobolev regularity of partial differential equations

Cite

@article{arxiv.2202.10867,
  title  = {Subelliptic estimates for the $\bar{\partial}$-problem on complex algebraic surfaces with isolated singularities},
  author = {Dariush Ehsani},
  journal= {arXiv preprint arXiv:2202.10867},
  year   = {2022}
}