Semiglobal results for \(\overline{\partial}_b\) on weakly convex hypersurfaces in \(\mathbb{C}^n\) (Q1593022)
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scientific article; zbMATH DE number 1553598
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Semiglobal results for \(\overline{\partial}_b\) on weakly convex hypersurfaces in \(\mathbb{C}^n\) |
scientific article; zbMATH DE number 1553598 |
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Semiglobal results for \(\overline{\partial}_b\) on weakly convex hypersurfaces in \(\mathbb{C}^n\) (English)
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13 May 2001
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Let \(M\) be the boundary of a smoothly bounded weakly convex domain in \(\mathbb{C}^n\), \(n\geq 4\). The author derives a homotopy formula for \((0,q)\)-forms on certain smoothly bounded subsets \(w\) of \(M\), when \(1\leq q\leq n-2\). The homotopy operators satisfy estimates up to the boundary of \(w\). As a corollary, solvability of \(\overline \partial_b\) in \(C^\infty (\overline w)\) is obtained.
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weakly convex hypersurfaces
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\(\overline\partial_b\)
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homotopy formula
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