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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Regularity of the $ \overline\partial$-Neumann problem


Author: So-Chin Chen
Journal: Proc. Amer. Math. Soc. 111 (1991), 779-785
MSC: Primary 32F20; Secondary 35N15
MathSciNet review: 1049842
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Abstract: In this paper we prove that locally there is no obstruction to global regularity for the $ \bar \partial $-Neumann problem. By this we mean the following: Let $ D$ be a smoothly bounded pseudoconvex domain in $ {{\mathbf{C}}^n},n \geq 2$, and let $ p \in {\mathbf{D}}$. Given any $ m \in {{\mathbf{Z}}^ + }$, one can construct a smoothly bounded pseudoconvex subdomain $ {D_m}\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \subset } D$ such that $ b{D_m} \cap bD$ contains an open neighborhood of $ p$ in $ bD$ and the $ \bar \partial $-Neumann problem on $ {D_m}$ is globally regular up to order $ m$ in the sense of the Sobolev norm.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1049842-7
PII: S 0002-9939(1991)1049842-7
Keywords: Pseudoconvex domains, $ \bar \partial $-Neumann problems
Article copyright: © Copyright 1991 American Mathematical Society