On the Strong Attraction Limit for a Class of Nonlocal Interaction Energies

2019/11/06 by Almut Burchard, Burchard, Almut, Rustum Choksi +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1911.02539

14 pages, 10 figures

arxiv created 2020/03/04 · arxiv updated 2020/03/05

Abstract

This note concerns the problem of minimizing a certain family of non-local energy functionals over measures on ℝⁿ, 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 in high dimensions.

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