## Illinois Journal of Mathematics

### Good Stein neighborhood bases and regularity of the $\overline\partial$-Neumann problem

Emil J. Straube

#### Abstract

We show that the $\bar\partial$-Neumann problem is globally regular on a smooth bounded pseudoconvex domain in $\mathbb{C}^{n}$ whose closure admits a sufficiently nice Stein neighborhood basis. We also discuss (what turns out to be) a generalization: global regularity holds as soon as the weakly pseudoconvex directions at boundary points are limits, from inside, of weakly pseudoconvex directions of level sets of the boundary distance.

#### Article information

Source
Illinois J. Math., Volume 45, Number 3 (2001), 865-871.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138156

Digital Object Identifier
doi:10.1215/ijm/1258138156

Mathematical Reviews number (MathSciNet)
MR1879240

Zentralblatt MATH identifier
0997.32038

#### Citation

Straube, Emil J. Good Stein neighborhood bases and regularity of the $\overline\partial$-Neumann problem. Illinois J. Math. 45 (2001), no. 3, 865--871. doi:10.1215/ijm/1258138156. https://projecteuclid.org/euclid.ijm/1258138156