충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제32권1호
  • /
  • Pages.23-28
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  • 2019
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  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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ON MINIMIZERS FOR THE INTERACTION ENERGY WITH MILDLY REPULSIVE POTENTIAL

  • Kim, Hwa Kil (Department of Mathematics Education Hannam University)
  • 투고 : 2018.10.24
  • 심사 : 2018.11.19
  • 발행 : 2019.02.15
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초록

In this paper, we consider an interaction energy with attractive-repulsive potential. We survey recent results on the structure of global minimizers for the mildly repulsive interaction energy. We introduce a theorem which is important to the proof of the above results, and give a detailed proof of the theorem.

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참고문헌

  1. D. Balague, J. A. Carrillo, T. Laurent, and G. Raoul, Dimensionality of Local Minimizers of the Interaction Energy, Arch. Rational Mech. Anal, 209 (2013), 1055-1088. https://doi.org/10.1007/s00205-013-0644-6
  2. J. A. Carrillo, A. Figalli, and F.S.Patacchini, Geometry of minimizers for the interaction energy with mildly repulsive potentials, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 34 (2017), 1299-1308. https://doi.org/10.1016/j.anihpc.2016.10.004
  3. K. Kang, H. K. Kim, and G. Seo, Cardinality estimation of global minimizer for interaction energy with mildly repulsive potentials, Preprint.