We consider here two well-known variational problems associated with the phenomenon of phase separation: the isoperimetric problem and minimization of the Cahn-Hilliard energy. The two problems are related through a classical result in Γ -convergence and we explore the behavior of global and local minimizers for these problems in the periodic setting. More precisely, we investigate these variational problems for competitors defined on the flat 2 or 3-torus. We view these two problems as prototypes for periodic phase separation. We give here a complete analysis of stable critical points of the 2-d periodic isoperimetric problem and also obtain stable solutions to the 2-d and 3-d periodic Cahn-Hilliard problem. We also discuss some intriguing open questions regarding triply periodic constant mean curvature surfaces in 3d and possible counterparts in the Cahn-Hilliard setting.
1
Simon Fraser University, Burnaby, Canada
2
Indiana University, Bloomington, United States
Rustum Choksi; Peter Sternberg. Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems. Interfaces and free boundaries, Tome 8 (2006) no. 3, pp. 371-392. doi: 10.4171/ifb/148
@article{10_4171_ifb_148,
author = {Rustum Choksi and Peter Sternberg},
title = {Periodic phase separation: the periodic {Cahn-Hilliard} and isoperimetric problems},
journal = {Interfaces and free boundaries},
pages = {371--392},
year = {2006},
volume = {8},
number = {3},
doi = {10.4171/ifb/148},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/148/}
}
TY - JOUR
AU - Rustum Choksi
AU - Peter Sternberg
TI - Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems
JO - Interfaces and free boundaries
PY - 2006
SP - 371
EP - 392
VL - 8
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/148/
DO - 10.4171/ifb/148
ID - 10_4171_ifb_148
ER -
%0 Journal Article
%A Rustum Choksi
%A Peter Sternberg
%T Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems
%J Interfaces and free boundaries
%D 2006
%P 371-392
%V 8
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/148/
%R 10.4171/ifb/148
%F 10_4171_ifb_148
