Variational analysis of a mesoscale model for bilayer membranes

Luca Lussardi, Mark A. Peletier, Matthias Röger

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)217-240
Number of pages24
JournalJOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS
Volume15
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Lipid bilayers
  • Monge–Kantorovich distance
  • curvature functionals

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