Calculus of Variations and Geometric Measure Theory

J. A. Carrillo - A. Figalli - F. S. Patacchini

Geometry of minimizers for the interaction energy with mildly repulsive potentials

created by figalli on 04 Oct 2016
modified on 08 May 2017


Accepted Paper

Inserted: 4 oct 2016
Last Updated: 8 may 2017

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2016


We show that the support of any local minimizer of the interaction energy consists of isolated points whenever the interaction potential is of class $C^2$ 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.