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

• Autorzy: Laskowski, W. , Nguyen, H. T.
• Języki publikacji: EN

Abstrakty

EN

We consider an elastic thin film as a bounded open subset ω of R2. First, the effective energy functional for the thin film ω is obtained, by Γ-convergence and 3D-2D dimension reduction techniques applied to the sequence of re-scaled total energy integral functionals of the elastic cylinders (…) 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 (…) and (…) (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) = (…) for some (…).

Słowa kluczowe

PL

gamma-zbieżność; Γ-zbieżność; zmniejszenie wymiaru 3D-2D; cienkie warstwy; membrana elastyczna; masa powierzchniowa; energia powierzchniowa; stan równowagi; przestrzeń Orlicza; przestrzeń Orlicza-Soboleva

EN

Γ-convergence; 3D-2D dimension reduction; quasiconvex relaxation; minimizers of variational integral functionals; thin films; elastic membrane; effective energy integral functional; bulk energy; surface energy; equilibrium state; non-power-growth-type bulk energy density; Orlicz space; Orlicz-Sobolev space

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 3
• Strony: 585--604
• Opis fizyczny: Bibliogr. 34 poz.

Twórcy

autor

Laskowski, W.

• School of Mathematics, West Pomeranian University of Technology, Al. Piastów 48, 70-311 Szczecin, Poland,

autor

Nguyen, H. T.

• Institute of Mathematics, Szczecin University, ul. Wielkopolska 15, 70-451 Szczecin, Poland,

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