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首页> 外文期刊>Demonstratio Mathematica >Effective energy integral functionals for thin films in the Orlicz–Sobolev space setting
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Effective energy integral functionals for thin films in the Orlicz–Sobolev space setting

机译：Effective energy integral functionals for thin films in the Orlicz–Sobolev space setting

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摘要

We consider an elastic thin film as a bounded open subset ω of ℝ 2 . First, the effective energy functional for the thin film ω is obtained, by Г-convergence and 3 D -2 D dimension reduction techniques applied to the sequence of re-scaled total energy integral functionals of the elastic cylinders ω×(-ε2,ε2)$omega times left( { - {varepsilon over 2},{varepsilon over 2}} right)$ as the thickness ε goes to 0. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function for the elastic cylinders 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 ∇ 2 and ∇ 2 (that is equivalent to the reflexivity of Orlicz and Orlicz–Sobolev spaces generated by M ). These results extend results of H. Le Dret and A. Raoult for the case M ( t ) = t p for some p ∈ (1, ∞).

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