Continuity of critical points for 1-dimensional non-local energies

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.

References in corpus (3)

• Existence of Ground States of Nonlocal-Interaction Energies
• Classifying minimum energy states for interacting particles: Regular simplices
• On the existence of minimizing sets for a weakly-repulsive non-local energy