We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampére-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group.
@article{BUMI_2008_9_1_2_489_0,
author = {Martino Bardi and Paola Mannucci},
title = {Comparison Principles for Subelliptic Equations of Monge-Amp\`ere Type},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {1},
year = {2008},
pages = {489-495},
zbl = {1203.35081},
mrnumber = {2424306},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_2_489_0}
}
Bardi, Martino; Mannucci, Paola. Comparison Principles for Subelliptic Equations of Monge-Ampère Type. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 489-495. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_2_489_0/
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