The L2 ∂¯-Cauchy problem on pseudoconvex domains and applications

DOI10.1142/S1793557118500250zbMath1388.32028MaRDI QIDQ4609513

Sayed Saber

Publication date: 3 April 2018

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

weakly pseudoconvex domains\(\overline{\partial}\)-problem\(\overline{\partial}_b\)-problem

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Pseudoconvex domains (32T99) (overlinepartial_b) and (overlinepartial_b)-Neumann operators (32W10)

Related Items (1)

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Cites Work

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• Global regularity and spectra of Laplace-Beltrami operators on pseudoconvex domains
• Régularité pour \(\overline\partial\) dans quelques domaines faiblement pseudo-convexes
• Local existence theorems with estimates for \(\bar \partial_ b\) on weakly pseudo-convex CR manifolds
• Resolution of \(\overline{\partial}\) for continuable currents defined in a circular domain.
• Estimates for the \(\bar\partial\)-Neumann problem and nonexistence of \(C^2\) Levi-flat hypersurfaces in \(\mathbb{C} P^n\)
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• The $\bar \partial $-problem on q-pseudoconvex domains with applications
• The L 2 $$\overline \partial $$ -Cauchy problem on weakly q-pseudoconvex domains in Stein manifolds
• SOLUTION TO $\overline{\partial}$ PROBLEM WITH EXACT SUPPORT AND REGULARITY FOR THE $\overline{\partial}$-NEUMANN OPERATOR ON WEAKLY q-CONVEX DOMAINS
• Regularity of \(\overline{\partial}\) on pseudoconcave compacts and applications
• Closed range for \(\overline{\partial}\) and \(\overline{\partial}_b\) on bounded hypersurfaces in Stein manifolds

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