Un example de domaine pseudoconvexe ou l'équation \(\overline\partial u=f\) n'admet pas de solution bornée pour \(f\) bornée

DOI10.1007/BF01389159zbMath0429.32026MaRDI QIDQ1137700

Nessim Sibony

Publication date: 1980

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142771

zbMATH Keywords

weakly pseudoconvex domaindelta equationnot peak point

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Boundary behavior of holomorphic functions of several complex variables (32A40) Algebras of holomorphic functions of several complex variables (32A38) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items

Non-closed Range Property for the Cauchy-Riemann Operator ⋮ Hölder estimates on domains of complex dimension two and on three- dimensional CR manifolds ⋮ \(C^k\)-estimates for \(\bar{\partial}\)-equation on certain convex domains of infinite type in \(\mathbb{C}^n\) ⋮ Sharp pointwise and uniform estimates for \(\bar{\partial} \) ⋮ A note on multiplier algebras on reproducing kernel Hilbert spaces ⋮ Estimates for \(\overline{\partial}\) on domains in \(\mathbb{C}^n\) and \(\mathbb{CP}^n\) ⋮ A counterexample to the existence of peaking functions ⋮ Normed domains of holomorphy ⋮ Geometry of Strictly Convex Domains and an Application to the Uniform Estimate of the $\overline\partial$-Problem ⋮ On Newton diagrams of plurisubharmonic polynomials

Cites Work

• A minimal boundary for function algebras
• Subellipticity of the \(\overline\partial\)-Neumann problem on pseudo- convex domains: sufficient conditions
• Holomorphic completions, analytic continuation, and the interpolation of semi-norms
• Hölder and L^p estimates for solutions of ∂u = f in strongly pseudoconvex domains
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
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