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

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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03325234
Contributor : Michael Goldman Connect in order to contact the contributor
Submitted on : Tuesday, August 24, 2021 - 3:12:32 PM
Last modification on : Thursday, August 26, 2021 - 3:33:37 AM

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  • HAL Id : hal-03325234, version 1
  • ARXIV : 2108.11102
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Jules Candau-Tilh, Michael Goldman. Existence and stability results for an isoperimetric problem with a non-local interaction of Wasserstein type. 2021. ⟨hal-03325234⟩

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