Volume 19, Number 4, October-December 2013
|Page(s)||1014 - 1029|
|Published online||26 July 2013|
Global minimizers for axisymmetric multiphase membranes
1 Department of Mathematics and
Statistics, McGill University, 805
Sherbrooke Street West, Montreal, Quebec,
2 Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA
3 Department of Mathematics “F. Casorati”, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy
Revised: 4 October 2012
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.
Mathematics Subject Classification: 49Q10 / 49J45 / (58E99, 53C80, 92C10)
Key words: Helfrich functional / biomembranes / global minimizers / axisymmetric surfaces / multicomponent vesicle
© EDP Sciences, SMAI, 2013
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