Comparison Principles for subelliptic equations of Monge-Ampere type

2008/02/11 by Bardi, Martino, Mannucci, Paola
#22E30 #35J60 #35J70 #49L25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0802.1456

Abstract

We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampere-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.

Related

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• Existence, uniqueness and interior regularity of viscosity solutions for a class of Monge-Ampère type equations
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• A strong comparison principle for the generalized Dirichlet problem for Monge-Ampere
• The comparsion principle for viscosity solutions of fully nonlinear subelliptic equations in Carnot groups