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Dimensionality of Local Minimizers of the Interaction Energy

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Abstract

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.

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Correspondence to D. Balagué.

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Communicated by D. Kinderlehrer

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Balagué, D., Carrillo, J.A., Laurent, T. et al. Dimensionality of Local Minimizers of the Interaction Energy. Arch Rational Mech Anal 209, 1055–1088 (2013). https://doi.org/10.1007/s00205-013-0644-6

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  • DOI: https://doi.org/10.1007/s00205-013-0644-6

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