On the strong attraction limit for a class of nonlocal interaction energies. (September 2020)

• Record Type: Journal Article
• Authors: Burchard, Almut; Choksi, Rustum; Hess-Childs, Elias
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: Nonlocal interaction energies -- Strong attraction limit -- Probability measures -- Γ-limit -- Body of constant width -- Capacity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111844
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This note concerns the problem of minimizing a certain family of non-local energy functionals over measures on R n, subject to a mass constraint, in a strong attraction limit. In these problems, the total energy is an integral over pair interactions of attractive-repulsive type. The interaction kernel is a sum of competing power law potentials with attractive powers α ∈ ( 0, ∞ ) and repulsive powers associated with Riesz potentials. The strong attraction limit α → ∞ is addressed via Gamma-convergence, and minimizers of the limit are characterized in terms of an isodiametric capacity problem. We also provide evidence for symmetry-breaking of minimizers in high dimensions.