Two-scale convergence with respect to measures and homogenization of monotone operators (Q558507)

The authors consider the two scales method in homogenization introduced in 1989 by Nguetseng. The two scale convergence with respect to a fixed periodic Borel measure has been introduced in 2000 by Zhikov in connection with the homogenization of periodically perforated domains. In the previous cases the spaces in consideration are \(L^2(\mu_\varepsilon)\) and \(H^1_0(\mu_\varepsilon)\). The author deals with the case of \(L^p(\mu_\varepsilon)\) and \(H^{1,p}_0(\mu_\varepsilon)\) with reference to the applications to nonlinear cases.