Cardinality estimation of support of the global minimizer for the interaction energy with mildly repulsive potentials

Kyungkeun Kang, Hwa Kil Kim, Geuntaek Seo

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)51-57
Number of pages7
JournalPhysica D: Nonlinear Phenomena
Volume399
DOIs
Publication statusPublished - 2019 Dec 1

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Global Minimizer
Cardinality
cards
Energy
Interaction
interactions
energy
Arbitrary
estimates
Estimate

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Cite this

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Cardinality estimation of support of the global minimizer for the interaction energy with mildly repulsive potentials. / Kang, Kyungkeun; Kim, Hwa Kil; Seo, Geuntaek.

In: Physica D: Nonlinear Phenomena, Vol. 399, 01.12.2019, p. 51-57.

Research output: Contribution to journalArticle

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