Inserted: 3 feb 2009
Last Updated: 15 dec 2009
Journal: Lect. Notes Semin. Interdiscip. Mat.
We study fully nonlinear partial differential equations involving the determinant of the Hessian matrix of the unknown function with respect to a family of vector fields that generate a Carnot group. We prove a comparison theorem among viscosity sub- and supersolutions, for subsolutions uniformly convex with respect to the vector fields.
Keywords: Carnot groups, Viscosity solutions, Monge-Ampère equations, Subelliptic PDEs