\(\overline\partial\)-equation on a lunar domain with mixed boundary conditions (Q2796081)
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scientific article; zbMATH DE number 6559880
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\overline\partial\)-equation on a lunar domain with mixed boundary conditions |
scientific article; zbMATH DE number 6559880 |
Statements
23 March 2016
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\(\overline\partial\)-equation
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\(L^2\)-estimates
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Neumann boundary conditions
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0.8841619
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0.8583467
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0.85679585
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0.8452593
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0.8438343
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\(\overline\partial\)-equation on a lunar domain with mixed boundary conditions (English)
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The authors study the \(\overline \partial \)-equation for \((0,q)\)-forms on a special type of non-smooth domain, called a lunar domain, in a complex manifold with mixed boundary conditions. They establish an \(L^2\)- estimate and derive a Hodge-type decomposition theorem. Basically they follow the approach of \textit{D. Catlin} [J. Geom. Anal. 4, No. 4, 467--538 (1994; Zbl 0841.32012)]. They indicate that one cannot expect that the \(\overline \partial \)-equation is always solvable and show that the obstruction is of finite dimension in certain sense.
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