Minimizers for a one-dimensional interaction energy. (March 2022)

• Record Type: Journal Article
• Authors: Frank, Rupert L.
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: Minimization problem -- Interaction energy -- Explicit solution; 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.2021.112691
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modeling 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.