Phase Separation on Varying Surfaces and Convergence of Diffuse Interface Approximations

This work is motivated by Jülicher-Lipowsky type variational models for phase separated biomembranes, where a curvature energy for the overall shape is coupled to a line tension energy for the phase interfaces. We considers diffuse approximations where the line tension contribution is replaced by a Modica–Mortola type energy. Our approach uses the concept of BV functions over rectifiable currents introduced by Anzellotti, Delladio and Scianna [Annali di Matematica Pura ed Applicata, 1996]. (This is joint work with Heiner Olbermann, UC Louvain)