JournalsaihpcVol. 34, No. 5pp. 1299–1308

Geometry of minimizers for the interaction energy with mildly repulsive potentials

  • J.A. Carrillo

    Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

  • A. Figalli

    ETH Zürich, Department of Mathematics, Rämistrasse 101, CH-8092 Zürich, Switzerland

  • F.S. Patacchini

    Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Geometry of minimizers for the interaction energy with mildly repulsive potentials cover
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Abstract

We show that the support of any local minimizer of the interaction energy consists of isolated points whenever the interaction potential is of class and mildly repulsive at the origin; moreover, if the minimizer is global, then its support is finite. In addition, for some class of potentials we prove the validity of a uniform upper bound on the cardinal of the support of a global minimizer. Finally, in the one-dimensional case, we give quantitative bounds.

Cite this article

J.A. Carrillo, A. Figalli, F.S. Patacchini, Geometry of minimizers for the interaction energy with mildly repulsive potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 5, pp. 1299–1308

DOI 10.1016/J.ANIHPC.2016.10.004