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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	37
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	28
DOIs	https://doi.org/10.1051/cocv/2022040
Publication status	Published - 1 Jan 2022
Externally published	Yes

Keywords

Existence of minimizers
Non-local isoperimetric problem
Optimal transport

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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

M3 - Article

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JF - ESAIM - Control, Optimisation and Calculus of Variations

M1 - 37

ER -

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

Abstract

Keywords

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