Pointwise $C^{2,\alpha}$ estimates at the boundary for the Monge-Ampere equation

TL;DR

This paper establishes pointwise $C^{2,eta}$ regularity estimates at boundary points for solutions to the Monge-Ampère equation, given certain local conditions on data.

Contribution

It provides new boundary regularity results for the Monge-Ampère equation under specific local conditions.

Findings

Boundary $C^{2,eta}$ estimates obtained

Conditions on data are sufficient for regularity

Enhances understanding of boundary behavior in Monge-Ampère solutions

Abstract

We obtain pointwise $C^{2,\alpha}$ estimates at boundary points for solutions to the Monge-Ampere equation under appropriate local conditions on the right hand side and boundary data.