Comparison principles for subelliptic equations of Monge-Ampère type

Gevrey regularity of subelliptic Monge-Ampère equations in the plane

Regularity of Subelliptic Monge-ampère Equations in the Plane

We establish a C∞ regularity result for C1,1 solutions of degenerate Monge-Ampère equation in R2, under the assumption that the trace of the Hessian is bounded from below.

Comparison principles for equations of Monge-Ampère type in Carnot groups: a direct proof

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 suband supersolutions, for subsolutions uniformly convex with respect to the vector fields.

Comparison principles and Dirichlet problem for equations of Monge-Ampère type associated to vector fields∗

We study partial differential equations of Monge-Ampère type involving the derivates with respect to a family X of vector fields of Carnot type. The main result is a comparison principle among viscosity subsolutions, convex with respect to X , and viscosity supersolutions (in a weaker sense than usual), which implies the uniqueness of solution to the Dirichlet problem. Its assumptions include t...

Comparison principles and Dirichlet problem for fully nonlinear degenerate equations of Monge-Ampère type∗

We study fully nonlinear partial differential equations of Monge-Ampère type involving the derivates with respect to a family X of vector fields. The main result is a comparison principle among viscosity subsolutions, convex with respect to X , and viscosity supersolutions (in a weaker sense than usual), which implies the uniqueness of solution to the Dirichlet problem. Its assumptions include ...