Kolodziej's subsolution theorem for unbounded pseudoconvex domains
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Kolodziej's subsolution theorem for unbounded pseudoconvex domains
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RIS BIB ENDNOTEKolodziej's subsolution theorem for unbounded pseudoconvex domains
Publication date: 14.06.2013
Universitatis Iagellonicae Acta Mathematica, 2012, Volume 50, pp. 7-23
https://doi.org/10.4467/20843828AM.12.001.1119Authors
Kolodziej's subsolution theorem for unbounded pseudoconvex domains
In this paper we generalize Kolodziej's subsolution theorem to bounded and unbounded pseudoconvex domains, and in that way we are able to solve complex Monge-Ampère equations on general pseudoconvex domains. We then give a negative answer to a question of Cegrell and Kolodziej by constructing a compactly supported Radon measure µ that vanishes on all pluripolar sets in Cn such that µ(Cn) = (2π)n, and forwhich there is no function u in L+ such that (ddcu)=µ. We end this paper by solving a Monge-Ampère type equation. Furthermore, we proveuniqueness and stability of the solution.
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Information: Universitatis Iagellonicae Acta Mathematica, 2012, Volume 50, pp. 7-23
Article type: Original article
Titles:
Kolodziej's subsolution theorem for unbounded pseudoconvex domains
Kolodziej's subsolution theorem for unbounded pseudoconvex domains
Umea University Department of Mathematics and Mathematical Statistics Sweden
Institute of Mathematics, Jagiellonian University, Cracow, Poland
Published at: 14.06.2013
Article status: Open
Licence: None
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