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, lead- ing 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 gen- eral lower estimate and formally identify a curvature energy in the zero- thickness limit. Secondly we construct a recovery sequence and prove a matching upper-bound estimate.
Lussardi, L., Röger, M., Peletier, M. A., Variational analysis of a mesoscale model for bilayer membranes, <<JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS>>, 2014; 15 (Marzo): 217-240. [doi:10.1007/s11784-014-0180-5] [http://hdl.handle.net/10807/61085]
Variational analysis of a mesoscale model for bilayer membranes
Lussardi, Luca;
2014
Abstract
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, lead- ing 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 gen- eral lower estimate and formally identify a curvature energy in the zero- thickness limit. Secondly we construct a recovery sequence and prove a matching upper-bound estimate.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.