An analytic proof of the Krylov estimates for the complex Monge-Ampere equation and applications

TL;DR

This paper presents an analytic proof of Krylov's estimates for the complex Monge-Ampère equation, establishing optimal regularity results for extremal functions with nonconstant boundary conditions.

Contribution

It provides a new analytic proof of Krylov's estimates and applies these results to achieve optimal regularity for extremal functions.

Findings

Proved Krylov's estimates analytically for complex Monge-Ampère equations.

Established optimal regularity for extremal functions with nonconstant boundary data.

Abstract

We provide an analytic proof of a theorem of Krylov dealing with global $C^{1,1}$ estimates to solutons of degenerate complex Monge-Amp\`ere equations. As an application we show optimal regularity for various extremal functions with nonconstant boundary values.