Illinois Journal of Mathematics

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

Emil J. Straube

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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

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

First available in Project Euclid: 13 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]


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.

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