Remark on a nonlocal isoperimetric problem. (May 2017)

• Record Type: Journal Article
• Authors: Julin, Vesa
• Is Part Of: Nonlinear analysis. Volume 154(2017)
• Page Start: 174
• Page End: 188
• Publication Date: 2017-05
• Subjects: 49Q10 -- 49Q20 -- 82B24; Isoperimetric problem -- Shape optimization -- Critical points; 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.2016.10.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider isoperimetric problem with a nonlocal repulsive term given by the Newtonian potential. We prove that regular critical sets of the functional are analytic. This optimal regularity holds also for critical sets of the Ohta–Kawasaki functional. We also prove that when the strength of the nonlocal part is small the ball is the only possible stable critical set.