We consider a Canham - Helfrich - type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham - Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous results for a single phase [R. Choksi and M. Veneroni, Calc. Var. Partial Differ. Equ. (2012). DOI:10.1007/s00526-012-0553-9] and prove existence of a global minimizer.
Keywords: helfrich functional, biomembranes, global minimizers, axisymmetric surfaces, multicomponent vesicle
@article{COCV_2013__19_4_1014_0,
author = {Choksi, Rustum and Morandotti, Marco and Veneroni, Marco},
title = {Global minimizers for axisymmetric multiphase membranes},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1014--1029},
year = {2013},
publisher = {EDP Sciences},
volume = {19},
number = {4},
doi = {10.1051/cocv/2012042},
mrnumber = {3182678},
zbl = {1283.49048},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2012042/}
}
TY - JOUR AU - Choksi, Rustum AU - Morandotti, Marco AU - Veneroni, Marco TI - Global minimizers for axisymmetric multiphase membranes JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 1014 EP - 1029 VL - 19 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2012042/ DO - 10.1051/cocv/2012042 LA - en ID - COCV_2013__19_4_1014_0 ER -
%0 Journal Article %A Choksi, Rustum %A Morandotti, Marco %A Veneroni, Marco %T Global minimizers for axisymmetric multiphase membranes %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 1014-1029 %V 19 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2012042/ %R 10.1051/cocv/2012042 %G en %F COCV_2013__19_4_1014_0
Choksi, Rustum; Morandotti, Marco; Veneroni, Marco. Global minimizers for axisymmetric multiphase membranes. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 4, pp. 1014-1029. doi: 10.1051/cocv/2012042
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