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- Title
KOŁODZIEJ'S SUBSOLUTION THEOREM FOR UNBOUNDED PSEUDOCONVEX DOMAINS.
- Authors
ÅHAG, PER; CZYŻ, RAFAŁ
- Abstract
In this paper we generalize Kołodziej'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 Kołodziej by constructing a compactly supported Radon measure μ that vanishes on all pluripolar sets in Cn such that μ(Cn) = (2π)n, and for which there is no function u in L+ such that (ddcu)n = μ. We end this paper by solving a Monge-Ampère type equation. Furthermore, we prove uniqueness and stability of the solution.
- Subjects
PSEUDOCONVEX domains; MONGE-Ampere equations; RADON transforms; PARTIAL differential equations; PERRON, Oscar
- Publication
Universitatis Iagellonicae Acta Mathematica, 2012, Vol 50, p7
- ISSN
0083-4386
- Publication type
Article
- DOI
10.4467/20843828AM.12.001.1119