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

Włodzimierz Laskowski; Hong Thai Nguyen

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2016)

  • Volume: 36, Issue: 1, page 7-31
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Włodzimierz Laskowski, and Hong Thai Nguyen. "Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 36.1 (2016): 7-31. <http://eudml.org/doc/286877>.

@article{WłodzimierzLaskowski2016,
abstract = {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.},
author = {Włodzimierz Laskowski, Hong Thai Nguyen},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Γ-convergence; 3D-2D dimension reduction; quasiconvex relaxation; minimizers of variational integral functionals; thin films; elastic membranes; effective energy integral functional; bulk and surface energy; equilibrium states of the film; non-power-growth-type bulk energy density; reflexive Orlicz and Orlicz-Sobolev spaces; integral functionals; -convergence; Orlicz-Sobolev spaces},
language = {eng},
number = {1},
pages = {7-31},
title = {Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting},
url = {http://eudml.org/doc/286877},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Włodzimierz Laskowski
AU - Hong Thai Nguyen
TI - Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2016
VL - 36
IS - 1
SP - 7
EP - 31
AB - 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.
LA - eng
KW - Γ-convergence; 3D-2D dimension reduction; quasiconvex relaxation; minimizers of variational integral functionals; thin films; elastic membranes; effective energy integral functional; bulk and surface energy; equilibrium states of the film; non-power-growth-type bulk energy density; reflexive Orlicz and Orlicz-Sobolev spaces; integral functionals; -convergence; Orlicz-Sobolev spaces
UR - http://eudml.org/doc/286877
ER -

References

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