{
"id": "1911.02539",
"version": "v1",
"published": "2019-11-06T18:24:37.000Z",
"updated": "2019-11-06T18:24:37.000Z",
"title": "On the Strong Attraction Limit for a Class of Nonlocal Interaction Energies",
"authors": [
"Almut Burchard",
"Rustum Choksi",
"Elias Hess-Childs"
],
"comment": "12 pages, 7 figures",
"categories": [
"math.AP"
],
"abstract": "This note concerns the problem of minimizing a certain family of nonlocal energy functionals over measures on $\\mathbb{R}^n$, 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 $\\alpha\\in(0,\\infty)$ and repulsive powers associated with Riesz potentials. The strong attraction limit $\\alpha\\rightarrow\\infty$ is addressed via Gamma-convergence, and minimizers of the limit are characterized in terms of an isodiametric capacity problem.",
"revisions": [
{
"version": "v1",
"updated": "2019-11-06T18:24:37.000Z"
}
],
"analyses": {
"keywords": [
"strong attraction limit",
"nonlocal interaction energies",
"isodiametric capacity problem",
"nonlocal energy functionals",
"competing power law potentials"
],
"note": {
"typesetting": "TeX",
"pages": 12,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}