# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1706.07392