Kolodziej's subsolution theorem for unbounded pseudoconvex domains

Per Åhag,

Rafał Czyż

Abstrakt

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 in Lsuch that (ddcu)=µ. We end this paper by solving a Monge-Ampère type equation. Furthermore, we proveuniqueness and stability of the solution.

Słowa kluczowe: Complex Monge-Ampère operator, plurisubharmonic function, Dirichlet problem
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