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We rigorously prove the convergence of weak solutions to a model for lipidraft formation in cell membranes which was recently proposed by Garcke et al.to weak (varifold) solutions of the corresponding sharp-interface problem for asuitable subsequence. In the system a Cahn-Hilliard type equation on theboundary of a domain is coupled to a diffusion equation inside the domain. Theproof builds on techniques developed by X. Chen for the corresponding resultfor the Cahn-Hilliard equation.

On the Sharp Interface Limit of a Model for Phase Separation on Biological Membranes