Convergence of an approximation for rotationally symmetric two-phase lipid bilayer membranes

Abstract

We consider a diffuse interface approximation for the lipid phases of rotationally symmetric two-phase bilayer membranes and rigorously derive its $\Gamma$-limit. In particular, we prove that limit vesicles are $C^1$ across interfaces, which justifies a regularity assumption that is widely made in formal asymptotic and numerical studies. Moreover, a limit membrane may consist of several topological spheres, which are connected at the axis of revolution and resemble complete buds of the vesicle.

References in corpus (2)

• Lipid membranes with free edges
• Kinks in two-phase lipid bilayer membranes

Cited by in corpus (8)

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• Conservation, convergence, and computation for evolving heterogeneous elastic wires
• Lower regularity assumption for an Euler-Lagrange equation on the contact line of the phase dependent Helfrich energy