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

Włodzimierz Laskowski, and Hôǹg Thái Nguyêñ. "Effective energy integral functionals for thin films with bending moment in the Orlicz-Sobolev space setting." Banach Center Publications 102.1 (2014): 143-167. <http://eudml.org/doc/282237>.

@article{WłodzimierzLaskowski2014,
abstract = {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,∞).},
author = {Włodzimierz Laskowski, Hôǹg Thái Nguyêñ},
journal = {Banach Center Publications},
keywords = {integral functionals; -convergence; thin films; Orlicz-Sobolev spaces},
language = {eng},
number = {1},
pages = {143-167},
title = {Effective energy integral functionals for thin films with bending moment in the Orlicz-Sobolev space setting},
url = {http://eudml.org/doc/282237},
volume = {102},
year = {2014},
}

TY - JOUR
AU - Włodzimierz Laskowski
AU - Hôǹg Thái Nguyêñ
TI - Effective energy integral functionals for thin films with bending moment in the Orlicz-Sobolev space setting
JO - Banach Center Publications
PY - 2014
VL - 102
IS - 1
SP - 143
EP - 167
AB - 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,∞).
LA - eng
KW - integral functionals; -convergence; thin films; Orlicz-Sobolev spaces
UR - http://eudml.org/doc/282237
ER -