# The complex Monge-Amp\`ere equation on weakly pseudoconvex domains

## TL;DR

This paper establishes boundary regularity results for solutions to the complex Monge-Ampère equation on weakly pseudoconvex domains, extending understanding of regularity under minimal assumptions on data and domain geometry.

## Contribution

It proves weak Hölder regularity up to the boundary for solutions with data in L^p on domains satisfying the f-property, applicable to finite and infinite type pseudoconvex domains.

## Key findings

- Boundary regularity of solutions established
- Applicable to a broad class of pseudoconvex domains
- Extends previous results to weaker data and domain conditions

## Abstract

We show here a "weak" H\"older-regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge-Amp\`{e}re equation with data in the $L^p$ space and the boundary of the domain satisfying an $f$-property. The $f$-property is a potential-theoretical condition which holds for all pseudoconvex domains of finite type and many examples of infinite type.