Boundary regularity for solutions to the linearized Monge-Amp\`ere equations

TL;DR

This paper establishes boundary regularity and Holder gradient estimates for solutions to the linearized Monge-Ampère equations, extending classical results to affine invariant settings under natural assumptions.

Contribution

It provides affine invariant boundary Holder gradient estimates for solutions to the linearized Monge-Ampère equations, generalizing Krylov's results.

Findings

Boundary Holder gradient estimates obtained

Regularity results established under natural assumptions

Affine invariance of the estimates demonstrated

Abstract

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