Existence and stability results for an isoperimetric problem with a non-local interaction of Wasserstein type

Jules Candau-Tilh; Michael Goldman

doi:10.1051/cocv/2022040

Existence and stability results for an isoperimetric problem with a non-local interaction of Wasserstein type

Jules Candau-Tilh
, Michael Goldman

PSL research University & IPSL
Laboratoire de Probabilités et Modèles Aléatoires

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Numéro d'article	37
journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	28
Les DOIs	https://doi.org/10.1051/cocv/2022040
état	Publié - 1 janv. 2022
Modification externe	Oui

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10.1051/cocv/2022040

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abstract = "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.",

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N2 - 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.

AB - 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.

KW - Existence of minimizers

KW - Non-local isoperimetric problem

KW - Optimal transport

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DO - 10.1051/cocv/2022040

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Existence and stability results for an isoperimetric problem with a non-local interaction of Wasserstein type

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