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

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

paper · pdf · doi:10.48550/arxiv.1911.02539

Abstract

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

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