preprint

Inserted: 5 aug 2026

Year: 2026

Abstract:

In dimension one, we introduce a one-parameter family of nonlocal energies, including subcritical Gagliardo seminorms and Riesz functionals, acting on scalar functions whose derivative is given by a periodic configuration of screened Dirac masses. We prove that the global minimizers are given by the equi-spaced configurations of particles. This result is achieved by representing the energy functionals as interaction potentials depending on the geodesic distances between the particles, exploiting the complete monotonicity properties of such potentials and invoking the celebrated Cohn-Kumar Universality Theorem.