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Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting

  • * Corresponding author: Elvira Zappale

    * Corresponding author: Elvira Zappale
The first and the last authors thank ICTP-INDAM Research in Pairs programme 2018
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  • 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.

    Mathematics Subject Classification: Primary: 49J45, 46J10; Secondary: 46E30.


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