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On Two-Scale Convergence

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Abstract

In this paper we present the foundations of the two-scale convergence theory. We discuss the class of “admissible” functions in the mean-value formula and in the definition of two-scale convergence. We discuss the relation between strong and weak convergence and prove general theorems on the semicontinuity from below for convex functionals, and we also discuss the relation between two-scale convergence and monotonicity. The explanations are conducted on the level of L p-convergence; we do not deal with convergence in Sobolev spaces.

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  1. V. V. Zhikov
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Zhikov, V.V. On Two-Scale Convergence. Journal of Mathematical Sciences 120, 1328–1352 (2004). https://doi.org/10.1023/B:JOTH.0000016052.48558.b4

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  • DOI: https://doi.org/10.1023/B:JOTH.0000016052.48558.b4

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