Stability and minimality of the ball for attractive-repulsive energies with perimeter penalization
Marco Bonacini
University of Trento, Povo (Trento), ItalyIhsan Topaloglu
Virginia Commonwealth University, Richmond, USA

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