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

Heungju Ahn

doi:10.1002/mana.200410486

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

Heungju Ahn

School of Undergraduate Studies

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

12 Scopus citations

Abstract

We introduce a notion of q-pseudoconvex domain of new type for a bounded domain of ℂⁿ and prove that for given a ∂̄-closed (p, r)-form, r ≥ q, that is smooth up to the boundary, there exists a (p, r - 1)-form smooth up to the boundary which is a solution of ∂̄-equation on a bounded q-pseudoconvex domain.

Original language	English
Pages (from-to)	343-350
Number of pages	8
Journal	Mathematische Nachrichten
Volume	280
Issue number	4
DOIs	https://doi.org/10.1002/mana.200410486
State	Published - 2007

Keywords

q-pseudoconvexity
∂̄-equation

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10.1002/mana.200410486

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

abstract = "We introduce a notion of q-pseudoconvex domain of new type for a bounded domain of ℂn and prove that for given a {\=∂}-closed (p, r)-form, r ≥ q, that is smooth up to the boundary, there exists a (p, r - 1)-form smooth up to the boundary which is a solution of {\=∂}-equation on a bounded q-pseudoconvex domain.",

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author = "Heungju Ahn",

year = "2007",

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language = "English",

volume = "280",

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journal = "Mathematische Nachrichten",

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T1 - Global boundary regularity for the ∂̄-equation on q-pseudoconvex domains

AU - Ahn, Heungju

PY - 2007

Y1 - 2007

N2 - We introduce a notion of q-pseudoconvex domain of new type for a bounded domain of ℂn and prove that for given a ∂̄-closed (p, r)-form, r ≥ q, that is smooth up to the boundary, there exists a (p, r - 1)-form smooth up to the boundary which is a solution of ∂̄-equation on a bounded q-pseudoconvex domain.

AB - We introduce a notion of q-pseudoconvex domain of new type for a bounded domain of ℂn and prove that for given a ∂̄-closed (p, r)-form, r ≥ q, that is smooth up to the boundary, there exists a (p, r - 1)-form smooth up to the boundary which is a solution of ∂̄-equation on a bounded q-pseudoconvex domain.

KW - q-pseudoconvexity

KW - ∂̄-equation

UR - https://www.scopus.com/pages/publications/33947128210

U2 - 10.1002/mana.200410486

DO - 10.1002/mana.200410486

M3 - Article

AN - SCOPUS:33947128210

SN - 0025-584X

VL - 280

SP - 343

EP - 350

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 4

ER -

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

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Keywords

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