Volume 28, 2022
|Number of page(s)||20|
|Published online||14 June 2022|
Existence and stability results for an isoperimetric problem with a non-local interaction of Wasserstein type
Ecole Normale Supérieure, ENS, 75005 Paris, France
2 Université de Paris, Sorbonne Université, Laboratoire Jacques-Louis Lions, LJLL, 75013 Paris, France
3 Université de Paris, Sorbonne Université, CNRS, Laboratoire Jacques-Louis Lions, LJLL, 75013 Paris, France
* Corresponding author: email@example.com
Accepted: 2 May 2022
The aim of this paper is to prove the existence of minimizers for a variational problem involving the minimization under volume constraint of the sum of the perimeter and a non-local energy of Wasserstein type. This extends previous partial results to the full range of parameters. We also show that in the regime where the perimeter is dominant, the energy is uniquely minimized by balls.
Mathematics Subject Classification: 49Q05 / 49Q20 / 49Q22
Key words: Non-local isoperimetric problem / optimal transport / existence of minimizers
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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