2014/02/26 by Luca Lussardi, Lussardi, Luca, Mark A. Peletier +3
Mathematics · #49J45 #49Q20 #74K15 #92C05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Stochastic processes and statistical mechanics #math.AP #msc:49J45 #msc:49Q20 #msc:74K15 #msc:92C05
paper · pdf · doi:10.48550/arxiv.1402.6600
arxiv created 2014/02/26 · openalex publication_date 2014/02/26 · arxiv updated 2014/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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 author (Arch. Ration. Mech. Anal. 193, 2009). The energy is both non-local and non-convex. 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 zero-thickness limit. Secondly we construct a recovery sequence and prove a matching upper-bound estimate.