Nonlocal Delaunay surfaces. (May 2016)

• Record Type: Journal Article
• Authors: Dávila, Juan; del Pino, Manuel; Dipierro, Serena; Valdinoci, Enrico
• Is Part Of: Nonlinear analysis. Volume 137(2016)
• Page Start: 357
• Page End: 380
• Publication Date: 2016-05
• Subjects: Delaunay surfaces -- Nonlocal perimeter -- Minimization problems; 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.2015.10.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We construct codimension 1 surfaces of any dimension that minimize a periodic nonlocal perimeter functional among surfaces that are periodic, cylindrically symmetric and decreasing. These surfaces may be seen as a nonlocal analogue of the classical Delaunay surfaces (onduloids). For small volume, most of their mass tends to be concentrated in a periodic array and the surfaces are close to a periodic array of balls (in fact, we give explicit quantitative bounds on these facts).