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

Kyungkeun Kang; Hwa Kil Kim; Geuntaek Seo

doi:10.1016/j.physd.2019.04.004

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

Kyungkeun Kang, Hwa Kil Kim, Geuntaek Seo

Department of Mathematics

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

3 Citations (Scopus)

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 language	English
Pages (from-to)	51-57
Number of pages	7
Journal	Physica D: Nonlinear Phenomena
Volume	399
DOIs	https://doi.org/10.1016/j.physd.2019.04.004
Publication status	Published - 2019 Dec 1

Bibliographical note

Funding Information:
Kyungkeun Kang’s work is supported by NRF, Republic of Korea - 2017R1A2B4006484 and NRF, Republic of Korea - 2015R1A5A1009350 . Hwa Kil Kim’s work was supported by NRF, Republic of Korea - 2018R1D1A1B07049357 . Geuntaek Seo’s work was partially supported by the Graduate School of YONSEI University, Republic of Korea Research Scholarship Grants in 2018. The authors are thankful to the anonymous referees for valuable suggestions.

Publisher Copyright:
© 2019 Elsevier B.V.

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/j.physd.2019.04.004

Cite this

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title = "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.",

author = "Kyungkeun Kang and Kim, {Hwa Kil} and Geuntaek Seo",

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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