On Weak Convergence of Locally Periodic Functions
نویسنده
چکیده
We have not found proofs of these facts in the literature. The aim of this paper is to present such proofs. Moreover, we show that the first statement also holds for the case p = 1. The two facts described above are used in the proof of the reiterated homogenization result for monotone operators, see [14] and [15]. The solution uξh is used to define a sequence of functions similar to the ones in Tartar’s celebrated method of oscillated test functions (see e.g. the book [8]). The first fact described above in combination with compensated compactness is used to analyze the asymptotic behavior of this sequence of functions. For information concerning reiterated homogenization we recommend the papers [14] and [15] and the references given there. Concerning explicit engineering applications see e.g. [4].
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