Wasserstein 型非局部相互作用的极大元
偏微分方程分析
2024-09-16 v2
摘要
我们刻画了一个泛函的极大元，该泛函涉及等体积集合间 Wasserstein 距离的最小化。我们通过结合反射对称化技术与最优传输计划的唯一性，证明球体是唯一的极大元。此外，在一维情形中，我们给出了该极大性结果的尖锐定量改进。
关键词
引用
@article{arxiv.2309.05522,
title = {Maximizers of nonlocal interactions of Wasserstein type},
author = {Almut Burchard and Davide Carazzato and Ihsan Topaloglu},
journal= {arXiv preprint arXiv:2309.05522},
year = {2024}
}
备注
This is a post-peer-review, pre-copyedit version of an article published in ESAIM: Control, Optimisation and Calculus of Variations. The final authenticated version is available online (https://doi.org/10.1051/cocv/2024068)