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 W 1,p (Ω; ℝ m ). 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.
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Braides et al. (1995) studied this question.
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