Variational analysis of a mesoscale model for bilayer membranes

We present an asymptotic analysis of a mesoscale energy for bilayer membranes that has been introduced and analyzed in two space dimensions by the second and third authors [Arch. Ration. Mech. Anal. 193 (2009), 475–537]. The energy is both nonlocal and nonconvex. It combines a surface area and a Monge–Kantorovich-distance term, leading to a competition between preferences for maximally concentrated and maximally dispersed configurations. Here we extend key results of our previous analysis to the three-dimensional case. First we prove a general lower estimate and formally identify a curvature energy in the zerothickness limit. Secondly we construct a recovery sequence and prove a matching upper-bound estimate.