Calculus of Variations and Geometric Measure Theory

J. Candau-Tilh - M. Goldman

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

created by goldman on 24 Aug 2021



Inserted: 24 aug 2021
Last Updated: 24 aug 2021

Year: 2021


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.