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

• Autorzy: Włodzimierz Laskowski , Hôǹg Thái Nguyêñ
• Języki publikacji: EN

Abstrakty

EN

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 ∇₂ (that is equivalent to the reflexivity of Orlicz and Orlicz-Sobolev spaces generated by M). These results extend results of G. Bouchitté, I. Fonseca and M. L. Mascarenhas for the case $M(t) = |t|^p$ for some p ∈ (1,∞).

Kategorie tematyczne

• 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytski{\u\i}, Uryson, etc.)
• 74K15: Membranes
• 49J45: Methods involving semicontinuity and convergence; relaxation
• 74B20: Nonlinear elasticity
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 74K35: Thin films

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 102
• Numer: 1
• Strony: 143-167

Daty

wydano

2014

Twórcy

autor

Włodzimierz Laskowski

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

autor

Hôǹg Thái Nguyêñ

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

Identyfikatory

DOI

10.4064/bc102-0-10