Geodesic
On a Monge–Ampère type equation in the Cegrell class $\mathcal{E}_{\chi}$
Rafa/l Czyż1
1 Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland
Annales Polonici Mathematici, Tome 99 (2010) no. 1, pp. 89-97 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $\Omega$ be a bounded hyperconvex domain in ${\mathbb C}{n}$ and let $\mu$ be a positive and finite measure which vanishes on all pluripolar subsets of $\Omega$. We prove that for every continuous and strictly increasing function $\chi:(-\infty,0) \to (-\infty,0)$ there exists a negative plurisubharmonic function $u$ which solves the Monge–Ampère type equation $$ -\chi(u)(dd^cu)^n = d\mu. $$ Under some additional assumption the solution $u$ is uniquely determined.
DOI : 10.4064/ap99-1-8
Keywords: omega bounded hyperconvex domain mathbb positive finite measure which vanishes pluripolar subsets omega prove every continuous strictly increasing function chi infty infty there exists negative plurisubharmonic function which solves monge amp type equation chi under additional assumption solution uniquely determined

Rafa/l Czyż 1

1 Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland 
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     title = {On a {Monge{\textendash}Amp\`ere} type equation in the {Cegrell} class $\mathcal{E}_{\chi}$},
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Rafa/l  Czyż. On a Monge–Ampère type equation in the Cegrell class $\mathcal{E}_{\chi}$. Annales Polonici Mathematici, Tome 99 (2010) no. 1, pp. 89-97. doi: 10.4064/ap99-1-8

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