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

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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.
  • School of Mathematics, West Pomeranian University of Technology, Al. Piastów 48, 70-311 Szczecin, Poland
  • Institute of Mathematics, Szczecin University, ul. Wielkopolska 15, 70-451 Szczecin, Poland
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