Let D be a domain in ℂⁿ. The plurisubharmonic envelope of a function φ ∈ C(D̅) is the supremum of all plurisubharmonic functions which are not greater than φ on D. A bounded domain D is called c-regular if the envelope of every function φ ∈ C(D̅) is continuous on D and extends continuously to D̅. The purpose of this paper is to give a complete characterization of c-regular domains in terms of Jensen measures.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-3-1,
author = {Nihat Gokhan Gogus},
title = {Continuity of plurisubharmonic envelopes},
journal = {Annales Polonici Mathematici},
volume = {85},
year = {2005},
pages = {197-217},
zbl = {1096.32017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-3-1}
}
Nihat Gokhan Gogus. Continuity of plurisubharmonic envelopes. Annales Polonici Mathematici, Tome 85 (2005) pp. 197-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap86-3-1/