Regularity of singular set in optimal transportation

• 成果类型: Article
• 署名作者: Chen, Shibing; Liu, Jiakun
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; University of Sydney
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01353-w
• 发表日期: 2025
• 页码: 1-44
• 关键词: boundary-value problem; MAPS

摘要

In this paper, we establish a regularity theory for the optimal transport problem when the target is composed of two disjoint convex domains. This is an important model in which singularities arise. Even though the singular set does not exhibit any form of convexity a priori, we prove its higher order regularity by developing novel methods, which also have many other applications. Notably, our results are achieved without requiring any convexity of the source domain. This aligns with Caffarelli's celebrated regularity theory.