Continuity of critical points for 1-dimensional non-local energies
Analysis of PDEs
2025-07-31 v1 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2507.22721,
title = {Continuity of critical points for 1-dimensional non-local energies},
author = {Davide Carazzato and Nicola Fusco and Aldo Pratelli},
journal= {arXiv preprint arXiv:2507.22721},
year = {2025}
}