Cardinality estimation of support of the global minimizer for the interaction energy with mildly repulsive potentials
Abstract
In this work, we give a cardinality estimation of the support of any global minimizer for the interaction energy with mildly repulsive potentials. For any global minimizer μ, the fact that supp(μ) consists of finitely many points was proved in Carrillo et al. (2017). Moreover, the authors found a cardinality estimation of the support of μ on R1. In order to advance some improvement of this result, we give an upper estimate of card(supp(μ)) in arbitrary finite dimension.
- Publication:
-
Physica D Nonlinear Phenomena
- Pub Date:
- December 2019
- DOI:
- 10.1016/j.physd.2019.04.004
- Bibcode:
- 2019PhyD..399...51K
- Keywords:
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- Wasserstein space;
- Interaction energy;
- Global minimizer