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.
Lingua originale | English |
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pagine (da-a) | 217-240 |
Numero di pagine | 24 |
Rivista | JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS |
Volume | 15 |
DOI | |
Stato di pubblicazione | Pubblicato - 2014 |
Pubblicato esternamente | Sì |
Keywords
- Lipid bilayers
- Monge–Kantorovich distance
- curvature functionals