Comparison Principles for subelliptic equations of Monge-Ampere type
Martino Bardi, Paola Mannucci
TL;DR
This paper establishes comparison principles for viscosity solutions of Monge-Ampere-type equations related to vector fields, ensuring uniqueness of solutions for the prescribed horizontal Gauss curvature problem in Carnot groups.
Contribution
It introduces two comparison principles for subelliptic Monge-Ampere equations, leading to the first uniqueness results for these equations in Carnot groups.
Findings
Established comparison principles for viscosity solutions.
Proved uniqueness of solutions for the Dirichlet problem.
Applied results to prescribed horizontal Gauss curvature equations.
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.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations