Regularity of weak solutions of a complex Monge-Amp\`ere equation

TL;DR

This paper proves that weak solutions to a complex Monge-Ampère equation are smooth, utilizing the smoothing effects of an associated parabolic flow to establish regularity.

Contribution

It introduces a method to demonstrate regularity of weak solutions by leveraging the smoothing properties of a related parabolic flow.

Findings

Weak solutions are shown to be smooth.

The parabolic flow technique effectively proves regularity.

The approach bridges elliptic and parabolic PDE methods.

Abstract

We prove the smoothness of weak solutions to an elliptic complex Monge-Ampere equation, using the smoothing property of the corresponding parabolic flow.