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arXiv · 1910.05778

Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting

Joel Fotso Tachago·Giuliano Gargiulo·Hubert Nnang·Elvira Zappale
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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\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 derivative are characterized in this setting.

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Joel Fotso Tachago, Giuliano Gargiulo, Hubert Nnang, Elvira Zappale. 2019-10-13. Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting. https://arxiv.org/abs/1910.05778

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