The $ \Gamma $-limit of a family of functionals $ u\mapsto \int_{\Omega }f\left( \frac{x}{\varepsilon },\frac{x}{\varepsilon ^{2}},D^{s}u\right) dx $ is obtained for $ s = 1,2 $ and when the integrand $ f = f\left( y,z,v\right) $ 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 derivatives are characterized in this setting.

中文翻译：

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Orlicz Sobolev环境中积分凸泛函的多尺度均质化

函数家族的$ \ Gamma $-极限$ u \ mapsto \ int _ {\ Omega} f \ left（\ frac {x} {\ varepsilon}，\ frac {x} {\ varepsilon ^ {2}}， D ^ {s} u \ right）dx $是为$ s = 1,2 $获得的，并且当被积数f = f \ left（y，z，v \ right）$是连续函数时，周期为$ y $和$ z $以及相对于$ v $的凸和非标准增长。在这种情况下，特征在于重申的二阶导数的二阶极限。