Effective energy integral functionals for thin films with bending moment in the Orlicz–Sobolev space setting
Volume 102 / 2014
Abstract
In this paper we deal with the energy functionals for the elastic thin film $\omega\subset \mathbb{R}^2$ involving the bending moments. The effective energy functional is obtained by $\Gamma$-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 $\Delta_{2}$ and $ \nabla_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 $p\in (1,\infty)$.
