DOI: 10.1515/acv-2025-0094 ISSN: 1864-8258
Continuity of critical points for 1-dimensional non-local energies
Davide Carazzato, Nicola Fusco, Aldo PratelliAbstract
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 origin, we are able to prove that they are continuous inside their support.