Dimensionality of Local Minimizers of the Interaction Energy

D. Balagué Guardia, Jose Antonio Carrillo, Thomas Laurent, Gael Raoul

Research output: Contribution to journalArticleScientificpeer-review


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.
Original languageEnglish
Pages (from-to)1055–1088
JournalArchive for Rational Mechanics and Analysis
Issue number3
Publication statusPublished - 2013
Externally publishedYes


  • Local Minimizer
  • Interaction Energy
  • Hausdorff dimension
  • Borel Probability Measure
  • Attractive Potential


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