Maximizers of nonlocal interactions of Wasserstein type
Analysis of PDEs
2024-09-16 v2
Abstract
We characterize the maximizers of a functional that involves the minimization of the Wasserstein distance between sets of equal volume. We prove that balls are the only maximizers by combining a symmetrization-by-reflection technique with the uniqueness of optimal transport plans. Further, in one dimension, we provide a sharp quantitative refinement of this maximality result.
Cite
@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}
}
Comments
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)