We modify an example due to X.-J. Wang and obtain some counterexamples to the regularity of the degenerate complex Monge-Ampère equation on a ball in ℂⁿ and on the projective space ℙⁿ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-2-7, author = {Szymon Pli\'s}, title = {A counterexample to the regularity of the degenerate complex Monge-Amp\`ere equation}, journal = {Annales Polonici Mathematici}, volume = {85}, year = {2005}, pages = {171-175}, zbl = {1136.32306}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-2-7} }
Szymon Pliś. A counterexample to the regularity of the degenerate complex Monge-Ampère equation. Annales Polonici Mathematici, Tome 85 (2005) pp. 171-175. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-2-7/