Variational models for pattern formation in biomembranes—A Γ‐convergence result

Abstract

Biological membranes are thin structures that are composed of various components. The different components often form microdomains, called lipid rafts, that are arranged in complex patterns. To explain this pattern formation, variational models based on Cahn–Hilliard‐type energies have been introduced that couple the local composition of the membrane to its local curvature, which renders the resulting functionals nonlocal. In this note, we review and extend recent qualitative results on related variational models. This includes a technique to deal with Neumann‐boundary conditions in the construction of a recovery sequence.