Illinois Journal of Mathematics

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

Emil J. Straube

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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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138156

Digital Object Identifier
doi:10.1215/ijm/1258138156

Mathematical Reviews number (MathSciNet)
MR1879240

Zentralblatt MATH identifier
0997.32038

Subjects
Primary: 32W05: $\overline\partial$ and $\overline\partial$-Neumann operators
Secondary: 32T99: None of the above, but in this section 35N15: $\overline\partial$-Neumann problem and generalizations; formal complexes [See also 32W05, 32W10, 58J10]

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


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