On a Monge-Ampère type equation in the Cegrell class ${}_{\chi }$

Rafał Czyż. "On a Monge-Ampère type equation in the Cegrell class $_{χ}$." Annales Polonici Mathematici 99.1 (2010): 89-97. <http://eudml.org/doc/280761>.

@article{RafałCzyż2010,
abstract = {Let Ω be a bounded hyperconvex domain in ℂn and let μ be a positive and finite measure which vanishes on all pluripolar subsets of Ω. We prove that for every continuous and strictly increasing function χ:(-∞,0) → (-∞,0) there exists a negative plurisubharmonic function u which solves the Monge-Ampère type equation $-χ(u)(dd^cu)ⁿ = dμ$. Under some additional assumption the solution u is uniquely determined.},
author = {Rafał Czyż},
journal = {Annales Polonici Mathematici},
keywords = {Monge-Ampère equation; plurisubharmonic function; comparison principle; stability theorems; energy classes},
language = {eng},
number = {1},
pages = {89-97},
title = {On a Monge-Ampère type equation in the Cegrell class $_\{χ\}$},
url = {http://eudml.org/doc/280761},
volume = {99},
year = {2010},
}

TY - JOUR
AU - Rafał Czyż
TI - On a Monge-Ampère type equation in the Cegrell class $_{χ}$
JO - Annales Polonici Mathematici
PY - 2010
VL - 99
IS - 1
SP - 89
EP - 97
AB - Let Ω be a bounded hyperconvex domain in ℂn and let μ be a positive and finite measure which vanishes on all pluripolar subsets of Ω. We prove that for every continuous and strictly increasing function χ:(-∞,0) → (-∞,0) there exists a negative plurisubharmonic function u which solves the Monge-Ampère type equation $-χ(u)(dd^cu)ⁿ = dμ$. Under some additional assumption the solution u is uniquely determined.
LA - eng
KW - Monge-Ampère equation; plurisubharmonic function; comparison principle; stability theorems; energy classes
UR - http://eudml.org/doc/280761
ER -