Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting

Laskowski, Włodzimierz ; Nguyen, Hong

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 1, pp. 7-31.

Résumé

In this paper we consider an elastic thin film ω ⊂ ℝ² with the bending moment depending also on the third thickness variable. The effective energy functional defined on the Orlicz-Sobolev space over ω is described by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type and to satisfy the conditions Δ₂ and ∇₂.

Détail

Keywords: Γ-convergence, 3D-2D dimension reduction, quasiconvex relaxation, minimizers of variational integral functionals, thin films, elastic membranes, effective energy integral functional, bulk and surface energy, equilibrium states of the film, non-power-growth-type bulk energy density, reflexive Orlicz and Orlicz-Sobolev spaces

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