Preprint

Inserted: 22 aug 2023
Last Updated: 22 aug 2023

Year: 2023

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.

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• Pattern formation in Biomembranes.pdf