Symmetry of constrained minimizers of the Cahn–Hilliard energy on the torus. (August 2020)

• Record Type: Journal Article
• Authors: Gelantalis, Michael; Wagner, Alfred; Westdickenberg, Maria G.
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: Cahn–Hilliard -- Steiner symmetrization -- Two-point rearrangement -- Bonnesen inequality; 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.2020.111842
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We establish sufficient conditions for a function on the torus to be equal to its Steiner symmetrization and apply the result to so-called volume-constrained minimizers of the Cahn–Hilliard energy. The resulting connectedness of superlevel sets is used in two dimensions together with the Bonnesen inequality to quantitatively estimate the sphericity of minimizers. We also show how two-point rearrangements can be used to give an alternate proof of symmetry for the constrained minimizers of the Cahn–Hilliard model.