Archive for Rational Mechanics and Analysis

, Volume 209, Issue 3, pp 1055–1088

Dimensionality of Local Minimizers of the Interaction Energy

  • D. Balagué
  • J. A. Carrillo
  • T. Laurent
  • G. Raoul

DOI: 10.1007/s00205-013-0644-6

Cite this article as:
Balagué, D., Carrillo, J.A., Laurent, T. et al. Arch Rational Mech Anal (2013) 209: 1055. doi:10.1007/s00205-013-0644-6


In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated with a repulsive–attractive potential. We show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • D. Balagué
    • 1
  • J. A. Carrillo
    • 2
  • T. Laurent
    • 3
  • G. Raoul
    • 4
  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Department of MathematicsImperial College LondonLondonUK
  3. 3.Department of MathematicsUniversity of California-RiversideRiversideUSA
  4. 4.Centre d’Ecologie Fonctionnelle et Evolutive, UMR 5175, CNRSMontpellier Cedex 5France

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