Maximizers of nonlocal interactions of Wasserstein type
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912026183335936 |
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| author | Burchard, Almut Carazzato, Davide Topaloglu, Ihsan |
| author_facet | Burchard, Almut Carazzato, Davide Topaloglu, Ihsan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05522 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximizers of nonlocal interactions of Wasserstein type Burchard, Almut Carazzato, Davide Topaloglu, Ihsan Analysis of PDEs 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. |
| title | Maximizers of nonlocal interactions of Wasserstein type |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2309.05522 |