Gamma convergence of a family of surface-director bending energies with small tilt

Luca Lussardi, Matthias Röger

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

2 Citazioni (Scopus)

Abstract

We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in R^3 equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and control the derivatives of the director. Such type of energies for example arise in a model for bilayer membranes introduced by Peletier and Roeger [Arch. Ration. Mech. Anal. 193 (2009)]. Here we prove in three space dimensions in the vanishing-tilt limit a Gamma-liminf estimate with respect to a specific curvature energy. In order to obtain appropriate compactness and lower semicontinuity properties we use tools from geometric measure theory, in particular the concept of generalized Gauss graphs and curvature varifolds.
Lingua originaleEnglish
pagine (da-a)985-1016
Numero di pagine32
RivistaArchive for Rational Mechanics and Analysis
Volume219
DOI
Stato di pubblicazionePubblicato - 2016

Keywords

  • Currents
  • Curvature functionals
  • Generalized Gauss graphs
  • Varifolds

Fingerprint Entra nei temi di ricerca di 'Gamma convergence of a family of surface-director bending energies with small tilt'. Insieme formano una fingerprint unica.

Cita questo