On a Monge-Ampère type equation in the Cegrell class $𝓔_{χ}$

• Autorzy: Rafał Czyż
• Języki publikacji: EN

Abstrakty

EN

Let Ω be a bounded hyperconvex domain in ℂn and let μ be a positive and finite measure which vanishes on all pluripolar subsets of Ω. We prove that for every continuous and strictly increasing function χ:(-∞,0) → (-∞,0) there exists a negative plurisubharmonic function u which solves the Monge-Ampère type equation
$-χ(u)(dd^cu)ⁿ = dμ$.
Under some additional assumption the solution u is uniquely determined.

Kategorie tematyczne

• 32U15: General pluripotential theory
• 32W20: Complex Monge-Amp\`ere operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2010
• Tom: 99
• Numer: 1
• Strony: 89-97

Daty

wydano

2010

Twórcy

autor

Rafał Czyż

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/ap99-1-8