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 (8)

• Isoperimetry and stability properties of balls with respect to nonlocal energies
• On an isoperimetric problem with a competing non-local term. II. The general case
• Existence of Compactly Supported Global Minimisers for the Interaction Energy
• On an isoperimetric problem with a competing non-local term. I. The planar case
• Existence of Ground States of Nonlocal-Interaction Energies
• Geometry of minimizers for the interaction energy with mildly repulsive potentials
• Classifying minimum energy states for interacting particles: Regular simplices
• On the existence of minimizing sets for a weakly-repulsive non-local energy