# Global regularity of optimal mappings in non-convex domains

## TL;DR

This paper proves a global regularity result for optimal transport maps with quadratic cost in non-convex domains, extending previous results from convex domains using a perturbation approach.

## Contribution

It introduces a novel perturbation method to establish regularity of optimal transport in non-convex domains, expanding the scope of existing regularity theory.

## Key findings

- Global regularity established for non-convex domains
- Perturbation technique effectively extends convex domain results
- Supports broader applications of optimal transport theory

## Abstract

In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.