Maximizers of nonlocal interactions of Wasserstein Type
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.
Authors
- Davide Carazzato (ORCID: https://orcid.org/0000-0001-7511-6698)
- Almut Burchard (ORCID: https://orcid.org/0000-0002-3542-1919)
- Ihsan Topaloğlu (ORCID: https://orcid.org/0000-0003-4584-156X)
Institutions
- Scuola Normale Superiore (IT)
- Virginia Commonwealth University (US)
- University of Toronto (CA)
Publication Details
- Journal
- ESAIM Control Optimisation and Calculus of Variations
- Published
- 2024-09-10
- DOI
- https://doi.org/10.1051/cocv/2024068
- Citations
- 1
- Primary Topic
- Spectral Theory in Mathematical Physics
- Type
- article
- Field-Weighted Citation Impact
- 0.89
Funders
- National Science Foundation
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Virginia Commonwealth University
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni