HOMOGENIZATION OF PERIODIC NONLINEAR MEDIA WITH STIFF AND SOFT INCLUSIONS
Andrea Braides, Adriana Garroni · Mathematical Models and Methods in Applied Sciences · 1995
We study the asymptotic behavior as ε→0 of highly oscillating periodic nonlinear functionals of the form [Formula: see text] defined on a Sobolev space W1,p(Ω; ℝm). We characterize their variational limit under the hypotheses that there exists a c such that the region where f(x, ξ)≤c(1+|ξ|p) does not hold for all matrices ξ is composed of well-separated sets, and the condition f(x, ξ)≥|ξ|p for all matrices ξ is verified on a connected open set with Lipschitz boundary.