Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting

The $Gamma $-limit of a family of functionals $umapsto int_{Omega }fleft( frac{x}{varepsilon },frac{x}{varepsilon ^{2}},D^{s}uright) dx$ is obtained for $s=1,2$ and when the integrand $f=fleft( y,z,vright) $ is a continous function, periodic in $y$ and $z$ and convex with respect to $v$ with nonstandard growth. The reiterated two-scale limits of second order derivative are characterized in this setting.