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.

引用

页数：23

共 50 条

[21] Global and Local Minimizers of the Cahn-Hilliard Functional Over a Parallelepiped: With And Without Constraint.
do Nascimento, Arnaldo Simal
Biesdorf, Joao
MILAN JOURNAL OF MATHEMATICS, 2011, 79 (01) : 303 - 310
[22] On Cahn-Hilliard systems with elasticity
Garcke, H
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2003, 133 : 307 - 331
[23] The convective Cahn-Hilliard equation
Eden, A.
Kalantarov, V. K.
APPLIED MATHEMATICS LETTERS, 2007, 20 (04) : 455 - 461
[24] ON CAHN-HILLIARD TYPE EQUATIONS
NOVICKCOHEN, A
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (09) : 797 - 814
[25] Nonhomogeneous Cahn-Hilliard fluids
Boyer, F
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2001, 18 (02): : 225 - 259
[26] On the Allen-Cahn/Cahn-Hilliard system with a geometrically linear elastic energy
Blesgen, Thomas
Schloemerkemper, Anja
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2014, 144 (02) : 241 - 266
[27] ON A COUPLED CAHN-HILLIARD/CAHN-HILLIARD MODEL FOR THE PROLIFERATIVE-TO-INVASIVE TRANSITION OF HYPOXIC GLIOMA CELLS
Li, Lu
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2021, 20 (04) : 1545 - 1557
[28] Existence and Properties of Certain Critical Points of the Cahn-Hilliard Energy
Gelantalis, Michael
Wagner, Alfred
Westdickenberg, Maria G.
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2017, 66 (05) : 1827 - 1877
[29] Energy Stable Numerical Schemes for Ternary Cahn-Hilliard System
Chen, Wenbin
Wang, Cheng
Wang, Shufen
Wang, Xiaoming
Wise, Steven M.
JOURNAL OF SCIENTIFIC COMPUTING, 2020, 84 (02)
[30] Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy
Abels, Helmut
Wilke, Mathias
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (11) : 3176 - 3193

← 1 2 3 4 5 →