Existence of minimizers for a generalized liquid drop model with fractional perimeter. (November 2022)

• Record Type: Journal Article
• Authors: Novaga, Matteo; Onoue, Fumihiko
• Is Part Of: Nonlinear analysis. Volume 224(2022)
• Publication Date: 2022-11
• Subjects: liquid drop model -- Fractional perimeter -- Generalized minimizers; 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.2022.113078
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the minimization problem of the functional given by the sum of the fractional perimeter and a general Riesz potential, which is one generalization of Gamow's liquid drop model. We first show the existence of minimizers for any volumes if the kernel of the Riesz potential decays faster than that of the fractional perimeter. We also prove the existence of generalized minimizers for any volumes if the kernel of the Riesz potential just vanishes at infinity. Finally, we study the asymptotic behavior of minimizers when the volume goes to infinity and we prove that a sequence of minimizers converges to the Euclidean ball up to translations if the kernel of the Riesz potential decays sufficiently fast.