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

被引：0
|
作者：
Gelantalis, Michael [1 ]
Wagner, Alfred [2 ]
Westdickenberg, Maria G. [2 ]
机构：
[1] Univ Tennessee Knoxville, Knoxville, TN USA
[2] Rhein Westfal TH Aachen, Aachen, Germany
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 197卷
关键词：
Cahn-Hilliard; Steiner symmetrization; Two-point rearrangement; Bonnesen inequality; REARRANGEMENTS; EXISTENCE; EQUATIONS;
D O I：
10.1016/j.na.2020.111842
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2020 Elsevier Ltd. All rights reserved.
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