Calculus of Variations and Geometric Measure Theory

D. Carazzato - N. Fusco - A. Pratelli

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

created by carazzato on 31 Jul 2025
modified on 25 Jun 2026

[BibTeX]

Published Paper

Inserted: 31 jul 2025
Last Updated: 25 jun 2026

Journal: Adv. Calc. Var.
Year: 2026
Doi: https://doi.org/doi:10.1515/acv-2025-0094

ArXiv: 2507.22721 PDF

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.