Geodesic
Some remarks on two-scale convergence and periodic unfolding
Applications of Mathematics, Tome 57 (2012) no. 4, pp. 359-375 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives ideas for generalization to non-periodic homogenization.
The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives ideas for generalization to non-periodic homogenization.
DOI : 10.1007/s10492-012-0021-z
Classification : 35B27, 35C20, 35J25
Keywords: two-scale convergence; unfolding; homogenization 
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     title = {Some remarks on two-scale convergence and periodic unfolding},
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Franců, Jan; Svanstedt, Nils E M. Some remarks on two-scale convergence and periodic unfolding. Applications of Mathematics, Tome 57 (2012) no. 4, pp. 359-375. doi: 10.1007/s10492-012-0021-z

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