A non local Monge-Ampere equation

Non Local Versions of the Monge Ampere Equation and of Symmetric Functions of the Hessian

Pointwise C Estimates at the Boundary for the Monge-ampere Equation

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.

A Liouville Theorem for Solutions to the Linearized Monge-ampere Equation

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 ∞.

GLOBAL W 2,p ESTIMATES FOR THE MONGE-AMPERE EQUATION

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.

Non Linear Elliptic Theory and the Monge-Ampere Equation

The Monge-Ampere equation, plays a central role in the theory of fully non linear equations. In fact we will like to show how the Monge-Ainpere equation, links in some way the ideas comming from the calculus of variations and those of the theory of fully non linear equations. 2000 Mathematics Subject Classification: 35J15, 35J20, 35J70. When learning complex analysis, it was a remarkable fact t...