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.

Lussardi, L., Roeger, M., Gamma convergence of a family of surface-director bending energies with small tilt, <<ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS>>, 2016; 219 (Marzo): 985-1016. [doi:10.1007/s00205-015-0914-6] [http://hdl.handle.net/10807/70108]

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

Lussardi, Luca;
2016

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.
Inglese
Lussardi, L., Roeger, M., Gamma convergence of a family of surface-director bending energies with small tilt, <>, 2016; 219 (Marzo): 985-1016. [doi:10.1007/s00205-015-0914-6] [http://hdl.handle.net/10807/70108]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/70108
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