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

TL;DR

This paper rigorously derives the limit behavior of a diffuse interface model for rotationally symmetric two-phase lipid bilayer membranes, establishing regularity and topological properties of the resulting vesicles.

Contribution

It provides a rigorous Gamma-convergence analysis for the approximation, confirming regularity and complex topologies of the limit membranes.

Findings

Limit vesicles are $C^1$ across interfaces.

Limit membranes can have multiple connected spherical components.

The analysis justifies assumptions used in numerical studies.

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.