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