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Pluripolar sets and subextension in Cegrell's classes
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2008 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, Vol. 53, no 7, 675-684 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we prove that if E is a complete pluripolar set in Ω, then E = { = −∞} for some  (Ω). Moreover, we study the subextension in Cegrell's class p .

Place, publisher, year, edition, pages
Taylor & Francis, 2008. Vol. 53, no 7, 675-684 p.
Keyword [en]
complex Monge-Ampére operator, plurisubharmonic function
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-2985DOI: 10.1080/17476930801966893OAI: oai:DiVA.org:umu-2985DiVA: diva2:141390
Available from: 2008-02-26 Created: 2008-02-26 Last updated: 2012-06-29Bibliographically approved
In thesis
1. Dirichlet's problem in Pluripotential Theory
Open this publication in new window or tab >>Dirichlet's problem in Pluripotential Theory
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we focus on Dirichlet's problem for the complex Monge-Ampère equation. That is, for a given non-negative Radon measure µ we are interested in the conditions under which there exists a plurisubharmonic function u such that (ddcu)n=µ, where (ddc)n is the complex Monge-Ampère operator. If this function u exists, then can it be chosen with given boundary values? Is this solution uniquely determined within a given class of functions?

Place, publisher, year, edition, pages
Umeå: Matematik och matematisk statistik, 2008. 19 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 40
Keyword
Complex Monge-Ampère operator, currents, Dirichlet problem, pluripotential theory, plurisubharmonic function, subextension
National Category
Mathematics
Identifiers
urn:nbn:se:umu:diva-1562 (URN)978-91-7264-443-4 (ISBN)
Public defence
2008-03-19, MA121, MIT, 901 87, Umeå, 10:15 (English)
Opponent
Supervisors
Available from: 2008-02-26 Created: 2008-02-26 Last updated: 2009-06-17Bibliographically approved

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Phạm, Hoàng Hiệp
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