HOMOGENIZATION OF PERIODIC NONLINEAR MEDIA WITH STIFF AND SOFT INCLUSIONS

We study the asymptotic behavior as epsilon --> 0 of highly oscillating periodic nonlinear functionals of the form F-epsilon(u) = integral(Omega)f(x/epsilon, Du(x)) dx, defined on a Sobolev space W-1,W-p(Omega;R(m)). We characterise their variational limit under the hypotheses that there exists a c such that the region where f(x,xi) less than or equal to c(1 + \xi\(p)) does not hold for all matrices xi is composed of well-separated sets, and the condition f(x,xi) greater than or equal to \xi\(p) for all matrices xi is verified on a connected open set with Lipschitz boundary.