Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting
Joel Fotso Tachago, Giuliano Gargiulo, Hubert Nnang, Elvira Zappale · Evolution equations and control theory · 2020
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.