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

Włodzimierz Laskowski;  Hôǹg Thái Nguyêñ — 2014

Banach Center Publications

In this paper we deal with the energy functionals for the elastic thin film ω ⊂ ℝ² involving the bending moments. The effective energy functional is obtained 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...

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

Włodzimierz Laskowski;  Hong Thai Nguyen — 2016

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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...

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