One can prove fairly sharp results on the existence of weak solutions to the complex Monge-Ampére equation applying the methods based on the concept of the positive current. We survey those results both in a strictly pseudoconvex domain and on a compact Kähler manifold.
@article{1656,
title = {The complex Monge-Amp\'ere equation and methods of pluripotential theory},
journal = {CUBO, A Mathematical Journal},
volume = {6},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/1656}
}
Kolodziej, Slawomir. The complex Monge-Ampére equation and methods of pluripotential theory. CUBO, A Mathematical Journal, Tome 6 (2004) . http://gdmltest.u-ga.fr/item/1656/