Homogenization and integral representation of energy functionals in manifold valued Orlicz-Sobolev spaces

This paper aims to extend to Orlicz-Sobolev spaces some results of integral representation for the simultaneous homogenization and dimensional reduction of integral energies defined on fields taking values on a differentiable manifold. Since our functional framework goes beyond the classical Sobolev’s spaces, we also prove, via $\mathrm{\Gamma }$-convergence, a general integral representation results in the unconstrained Orlicz setting. Due to ${\mathrm{\Delta }}_2$ and ${\mathrm{\nabla }}_2$ conditions verified by the Young function $\mathrm{\Phi }$ (which modulated the growth behaviour), we prove that the density of the $\mathrm{\Gamma }$-limit is a tangential quasiconvex integrand represented by a cell formula.