3 papers
math.AP2025
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…
math.AP2025
Continuity of critical points for 1-dimensional non-local energies
Davide Carazzato, Nicola Fusco, Aldo Pratelli
In this paper we deal with the bounded critical points of a Riesz energy of attractive-repulsive type in dimension 1. Under suitable assumptions on the growth of the kernel in the…
math.AP2024
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…