Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 80 | |
Number of page(s) | 25 | |
DOI | https://doi.org/10.1051/cocv/2024068 | |
Published online | 25 October 2024 |
Maximizers of nonlocal interactions of Wasserstein Type
1
Department of Mathematics, University of Toronto, ON, Canada
2
Scuola Normale Superiore, Pisa, Italy
3
Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond VA, USA
* Corresponding author: davide.carazzato@sns.it
Received:
25
September
2023
Accepted:
6
September
2024
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.
Mathematics Subject Classification: 49Q05 / 49Q20 / 49Q22 / 49J35
Key words: Max-min problem / optimal transport / symmetrization-by-reflection / Wasserstein distance
© The authors. Published by EDP Sciences, SMAI 2024
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