Using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of Monge-Amp`{e}re equations are established‎.‎

using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of monge-amp`{e}re equations are established‎.‎

using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of monge-amp`{e}re equations are established‎.‎

In this paper, by the method of moving planes, we prove the symmetry result which says that classical solutions of Monge-Ampere system in the whole plane are symmetric about some point. Our system under consideration comes from the differential geometry problem. Keyword: Moving plane, positive solutions, radial symmetric, MongeAmpere system Mathematics Subject Classification: 35J60, 53C21, 58J05

We introduce a non local analog to the Monge-Ampere operator and show some of its properties. We prove that a global problem involving this operator has C solutions in the full space.

We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution.

We prove a localization property of boundary sections for solutions to the Monge-Ampere equation. As a consequence we obtain pointwise C2,α estimates at boundary points under appropriate local conditions on the right hand side and boundary data.

We consider degenerate Monge-Ampere equations on compact Hessian manifolds. establish compactness properties of the set normalized quasi-convex functions and show local global comparison principles for twisted operators. then use Perron method to solve whose RHS involves an arbitrary probability measure, generalizing works Cheng-Yau, Delanoe, Caffarelli-Viaclovsky Hultgren-Onnheim. The intrinsi...

We prove that global Lipschitz solutions to the linearized MongeAmpere equation Lφu := ∑ φuij = 0 must be linear in 2D. The function φ is assumed to have the Monge-Ampere measure detD2φ bounded away from 0 and ∞.

We use a localization property of boundary sections for solutions to the Monge-Ampere equation and obtain global W 2,p estimates under natural assumptions on the domain and boundary data.