Global $W^{2,1+\epsilon}$ regularity for potentials of optimal transport of non-convex planar domains

TL;DR

This paper establishes a global regularity estimate for optimal transport potentials in non-convex planar domains, extending previous results to more general domain classes.

Contribution

It proves a global $W^{2,1+ ext{epsilon}}$ regularity for optimal transport potentials in non-convex planar domains, broadening the scope of regularity results.

Findings

Global $W^{2,1+\epsilon}$ regularity established

Applicable to a wider class of non-convex domains

Method extends previous convex domain results

Abstract

In this paper, we investigate the optimal transport problem when the source is a non-convex polygonal domain in $\mathbb{R}^2$. We show a global $W^{2,1+\epsilon}$ estimate for potentials of optimal transport. Our method applies to a more general class of domains.