Minimizers for a one-dimensional interaction energy
Mathematical Physics
2021-09-21 v1 Analysis of PDEs
math.MP
Optimization and Control
Abstract
We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modelling of aggregation phenomena. We show that in a certain regime minimizers are absolutely continuous with an unbounded density, thereby settling a question that was left open in previous works.
Keywords
Cite
@article{arxiv.2109.08929,
title = {Minimizers for a one-dimensional interaction energy},
author = {Rupert L. Frank},
journal= {arXiv preprint arXiv:2109.08929},
year = {2021}
}
Comments
12 pages