5 papers
The Liquid Drop Model with a Yukawa Potential: Existence of Minimizers and Sharp Stability of the Ball
Lia Bronsard, Kenneth DeMason, Ihsan Topaloglu
We study a long-range perturbation of the perimeter functional by a nonlocal repulsive term defined through the Yukawa kernel, minimized under a volume constraint. Because the kern…
Particle approximation of nonlocal interaction energies
Davide Carazzato, Aldo Pratelli, Ihsan Topaloglu
We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies -converg…
Stability and minimality of the ball for attractive-repulsive energies with perimeter penalization
Marco Bonacini, Ihsan Topaloglu
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…
A stability inequality for the planar lens partition
Marco Bonacini, Riccardo Cristoferi, Ihsan Topaloglu
Recently it has been shown that the unique locally perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infini…
On the existence of minimizing sets for a weakly-repulsive non-local energy
Davide Carazzato, Aldo Pratelli, Ihsan Topaloglu
We consider a non-local interaction energy over bounded densities of fixed mass . We prove that under certain regularity assumptions on the interaction kernel these energies adm…