Calibrations Associated to Monge-ampère Equations

Boundary Regularity for Solutions to the Linearized Monge-ampère Equations

We obtain boundary Hölder gradient estimates and regularity for solutions to the linearized Monge-Ampère equations under natural assumptions on the domain, Monge-Ampère measures and boundary data. Our results are affine invariant analogues of the boundary Hölder gradient estimates of Krylov.

Comparison principles for subelliptic equations of Monge-Ampère type

We present two comparison principles for viscosity suband supersolutions of Monge-Ampère-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.

Boundary Harnack Inequality for the Linearized Monge-ampère Equations and Applications

In this paper, we obtain boundary Harnack estimates and comparison theorem for nonnegative solutions to the linearized Monge-Ampère equations under natural assumptions on the domain, Monge-Ampère measures and boundary data. Our results are boundary versions of Caffarelli and Gutiérrez’s interior Harnack inequality for the linearized Monge-Ampère equations. As an application, we obtain sharp upp...

On normal forms for parabolic Monge-Ampère equations

Parabolic Monge-Ampère equations are divided into contact inequivalent classes, for each of which a normal form is given. Two of these are new in the C category.

Existence of convex solutions for systems of Monge-Ampère equations