Symmetry of constrained minimizers of the Cahn–Hilliard energy on the torus

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 in...

Full description

Saved in:
Bibliographic Details
Published inNonlinear analysis Vol. 197; p. 111842
Main Authors Gelantalis, Michael, Wagner, Alfred, Westdickenberg, Maria G.
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.08.2020
Elsevier BV
Subjects
Bonnesen inequality
Cahn–Hilliard
Set theory
Steiner symmetrization
Symmetry
Toruses
Two-point rearrangement
Cahn–Hilliard
Steiner symmetrization
Bonnesen inequality
Two-point rearrangement
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2020.111842