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 -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 μ in the class ℱ(Ω,g) without the assumption that μ vanishes on all pluripolar sets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-1-5,
author = {Le Mau Hai and Nguyen Xuan Hong},
title = {Subextension of plurisubharmonic functions without changing the Monge-Amp\`ere measures and applications},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {55-66},
zbl = {06330463},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-1-5}
}
Le Mau Hai; Nguyen Xuan Hong. Subextension of plurisubharmonic functions without changing the Monge-Ampère measures and applications. Annales Polonici Mathematici, Tome 111 (2014) pp. 55-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-1-5/