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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Global solvability and regularity for $ \bar \partial$ on an annulus between two weakly pseudoconvex domains


Author: Mei-Chi Shaw
Journal: Trans. Amer. Math. Soc. 291 (1985), 255-267
MSC: Primary 32F20; Secondary 35B65, 35N15
MathSciNet review: 797058
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Abstract: Let $ {M_1}$ and $ {M_2}$ be two bounded pseudo-convex domains in $ {{\mathbf{C}}^n}$ with smooth boundaries such that $ {\overline M _1} \subset {M_2}$. We consider the Cauchy-Riemann operators $ \overline \partial $ on the annulus $ M = {M_2}\backslash {\overline M _1}$. The main result of this paper is the following: Given a $ \overline \partial $-closed $ (p,q)$ form $ \alpha $, $ 0 < q < n$, which is $ {C^\infty }$ on $ \overline M $ and which is cohomologous to zero on $ M$, there exists a $ (p,q - 1)$ form $ u$ which is $ {C^\infty }$ on $ \overline M $ such that $ \overline \partial u = \alpha $.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0797058-3
PII: S 0002-9947(1985)0797058-3
Article copyright: © Copyright 1985 American Mathematical Society