Geodesic
Subextension of plurisubharmonic functions without changing the Monge–Ampère measures and applications
Le Mau Hai1 ; Nguyen Xuan Hong1
1 Department of Mathematics Hanoi National University of Education Hanoi, Vietnam
Annales Polonici Mathematici, Tome 112 (2014) no. 1, pp. 55-66.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The aim of the paper is to investigate subextensions with boundary values of certain plurisubharmonic functions without changing the Monge–Ampère measures. From the results obtained, we deduce that if a given sequence is convergent in $C_{n-1}$-capacity then the sequence of the Monge–Ampère measures of subextensions is weakly$^*$-convergent. As an application, we investigate the Dirichlet problem for a nonnegative measure $\mu $ in the class $\mathcal {F}(\varOmega ,g)$ without the assumption that $\mu $ vanishes on all pluripolar sets.
DOI : 10.4064/ap112-1-5
Keywords: the paper investigate subextensions boundary values certain plurisubharmonic functions without changing monge amp measures results obtained deduce given sequence convergent n capacity sequence monge amp measures subextensions weakly * convergent application investigate dirichlet problem nonnegative measure class mathcal varomega without assumption vanishes pluripolar sets

Le Mau Hai 1 ; Nguyen Xuan Hong 1

1 Department of Mathematics Hanoi National University of Education Hanoi, Vietnam 
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Le Mau Hai; Nguyen Xuan Hong. Subextension of plurisubharmonic functions without changing the Monge–Ampère measures and applications. Annales Polonici Mathematici, Tome 112 (2014) no. 1, pp. 55-66. doi : 10.4064/ap112-1-5. http://geodesic.mathdoc.fr/articles/10.4064/ap112-1-5/

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