Global boundary regularity for the ∂̄-equation on q-pseudoconvex domains

Heungju Ahn

Global boundary regularity for the ∂̄-equation on q-pseudoconvex domains

Heungju Ahn

School of Undergraduate Studies

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

For a bounded domain D of Cⁿ, we introduce a notion of «q-pseudoconvexity» of new type and prove that for a given ∂̄-closed (p, r)-form f that is smooth up to the boundary on D, and for r ≥ q, there exists a (p, r - l)-form u smooth up to the boundary on D which is a solution of the equation ∂̄u = f.

Original language	English
Pages (from-to)	5-9
Number of pages	5
Journal	Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume	16
Issue number	1
State	Published - 2005

Keywords

Cauchy-Riemann system
Q-pseudoconvexity
∂̄-equation

Cite this

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title = "Global boundary regularity for the {\=∂}-equation on q-pseudoconvex domains",

abstract = "For a bounded domain D of Cn, we introduce a notion of «q-pseudoconvexity» of new type and prove that for a given {\=∂}-closed (p, r)-form f that is smooth up to the boundary on D, and for r ≥ q, there exists a (p, r - l)-form u smooth up to the boundary on D which is a solution of the equation {\=∂}u = f.",

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year = "2005",

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journal = "Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni",

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AB - For a bounded domain D of Cn, we introduce a notion of «q-pseudoconvexity» of new type and prove that for a given ∂̄-closed (p, r)-form f that is smooth up to the boundary on D, and for r ≥ q, there exists a (p, r - l)-form u smooth up to the boundary on D which is a solution of the equation ∂̄u = f.

KW - Cauchy-Riemann system

KW - Q-pseudoconvexity

KW - ∂̄-equation

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JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

IS - 1

ER -

Global boundary regularity for the ∂̄-equation on q-pseudoconvex domains

Abstract

Keywords

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