Stability and minimality of the ball for attractive-repulsive energies with perimeter penalization

  • Marco Bonacini

    University of Trento, Povo (Trento), Italy
  • Ihsan Topaloglu

    Virginia Commonwealth University, Richmond, USA
Stability and minimality of the ball for attractive-repulsive energies with perimeter penalization cover
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Abstract

We consider perimeter perturbations of a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. We prove that there exist curves in the perturbation-volume parameter space that separate stability/instability and global minimality/nonminimality regions of the ball, and provide a precise description of these curves for certain interaction kernels. In particular, we show that in small perturbation regimes there are (at least) two disconnected regions for the mass parameter in which the ball is stable, separated by an instability region.

Cite this article

Marco Bonacini, Ihsan Topaloglu, Stability and minimality of the ball for attractive-repulsive energies with perimeter penalization. Interfaces Free Bound. (2025), published online first

DOI 10.4171/IFB/548