We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in R3 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 types of energies arise, for example, in a model for bilayer membranes introduced by Peletier and Röger (Arch Ration Mech Anal 193(3), 475–537, 2009). Here we prove in three space dimensions in the vanishingtilt limit a Gamma-liminf estimate with respect to a specific curvature energy. In order to obtain appropriate compactness and lower semi-continuity properties we use tools from geometric measure theory, in particular the concept of generalized Gauss graphs and curvature varifolds.

Gamma Convergence of a Family of Surface–Director Bending Energies with Small Tilt / Lussardi, Luca; Röger, Matthias. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 219:3(2016), pp. 985-1016. [10.1007/s00205-015-0914-6]

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 R3 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 types of energies arise, for example, in a model for bilayer membranes introduced by Peletier and Röger (Arch Ration Mech Anal 193(3), 475–537, 2009). Here we prove in three space dimensions in the vanishingtilt limit a Gamma-liminf estimate with respect to a specific curvature energy. In order to obtain appropriate compactness and lower semi-continuity properties we use tools from geometric measure theory, in particular the concept of generalized Gauss graphs and curvature varifolds.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2665231