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ABOUT THE $\bar{\partial}$-EQUATION AT ISOLATED SINGULARITIES WITH REGULAR EXCEPTIONAL SET.
- Source :
- International Journal of Mathematics; Apr2009, Vol. 20 Issue 4, p459-489, 31p
- Publication Year :
- 2009
-
Abstract
- Let Y be a pure dimensional analytic variety in ℂ<superscript>n</superscript> with an isolated singularity at the origin such that the exceptional set X of a desingularization of Y is regular. The main objective of the present paper is to present a technique which allows us to determine obstructions to the solvability of the $\bar{\partial}$ equation in the L<superscript>2</superscript>, respectively L<superscript>∞</superscript>, sense on Y* = Y\{0} in terms of certain cohomology classes on X. More precisely, let Ω ⊂⊂ Y be a Stein domain with 0 ∈ Ω, Ω* = Ω\{0}. We give a sufficient condition for the solvability of the $\bar{\partial}$ equation in the L<superscript>2</superscript>-sense on Ω*; and in the L<superscript>∞</superscript> sense, if Ω is in addition strongly pseudoconvex. If Y is an irreducible cone, we also give some necessary conditions and obtain optimal Hölder estimates for solutions of the $\bar{\partial}$ equation. [ABSTRACT FROM AUTHOR]
- Subjects :
- ANALYTIC functions
COMPLEX variables
HOMOLOGY theory
EQUATIONS
PSEUDOCONVEX domains
Subjects
Details
- Language :
- English
- ISSN :
- 0129167X
- Volume :
- 20
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- International Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 37381216
- Full Text :
- https://doi.org/10.1142/S0129167X09005388