Year: 2019
Type: preprint
Abstract: In this paper, we obtain some regularities of the free boundary in optimal transportation with the quadratic cost. Our first result is about the $C^{1,α}$ regularity of the free boundary for optimal partial transport between convex domains for densities $f, g$ bounded from below and above. When $f, g \in C^α$, and $\partialΩ, \partialΩ^*\in C^{1,1}$ are far apart, by adopting our recent results on boundary regularity of Monge-Ampère equations \cite{CLW1}, our second result shows that the free boundaries are $C^{2,α}$. As an application, in the last we also obtain these regularities of the free boundary in an optimal transport problem with two separate targets.
Source: arXiv (Cornell University)
Authors: Chen, Shibing, Liu, Jiakun
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2990620990