POINTWISE C2,α ESTIMATES AT THE BOUNDARY FOR THE MONGE-AMPÈRE EQUATION.

The article discusses pointwise C^2,α estimates at boundary points under specific local conditions on the right hand side and boundary data. The result can be viewed as a boundary Schauder estimate for the Monge-Ampere equation which extends up to the boundary the pointwise interior C^2,α estimate Caffarelli (C2). These estimates are reportedly important when dealing with fourth order Monge-Amp`re type equations in geometry.