*Published Paper*

**Inserted:** 11 dec 2002

**Last Updated:** 12 jan 2004

**Journal:** Journal of Convex Analysis

**Volume:** 10

**Number:** 2

**Pages:** 325-350

**Year:** 2002

**Abstract:**

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 $f=f(x,y,v)$ is a
continuous function, periodic in $x$ and $y$, and convex with respect
to $v$. The $3$-scale limits of second order derivatives are
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