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Global minimizers for axisymmetric multiphasemembranes

Published online by Cambridge University Press:  26 July 2013

Rustum Choksi,
Marco Morandotti and
Marco Veneroni
Rustum Choksi
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, H3A 2K6, Canada. rchoksi@math.mcgill.ca
Marco Morandotti
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA; marcomor@andrew.cmu.edu
Marco Veneroni
Affiliation:
Department of Mathematics “F. Casorati”, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy; marco.veneroni@unipv.it

Abstract

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We consider a Canham − Helfrich − type variational problem defined over closed surfacesenclosing a fixed volume and having fixed surface area. The problem models the shape ofmultiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrichenergy, in which the bending rigidities and spontaneous curvatures are nowphase-dependent, and a line tension penalization for the phase interfaces. By restrictingattention to axisymmetric surfaces and phase distributions, we extend our previous resultsfor 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 globalminimizer.

Keywords

Helfrich functionalbiomembranesglobal minimizersaxisymmetric surfacesmulticomponent vesicle

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 4 , October 2013, pp. 1014 - 1029
Copyright
© EDP Sciences, SMAI, 2013

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