A pseudoconvex domain with bounded solutions for \(\overline{\partial}\), but not admitting \({\mathcal C}^ 1\)-estimates

DOI10.1007/BF03025709zbMath0824.32005MaRDI QIDQ1319342

Joachim Michel

Publication date: 12 November 1995

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174517

zbMATH Keywords

pseudoconvex domainsHartogs triangle\(\overline (\partial)\)-equation

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Pseudoconvex domains (32T99) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Cites Work

• Régularité höldérienne de l'opérateur \(\bar\partial\) sur le triangle de Hartogs. (Hölder regularity of the \(\bar\partial\) operator on the Hartogs triangle.)
• \(\mathcal C^{k+\alpha}\)-estimates for the \(\bar \partial\)-equation on the Hartogs triangle
• A smooth pseudoconvex domain in \(\mathbb C^ 2\) for which \(L^ \infty\)- estimates for \(\overline\partial\) do not hold
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