## Alternative approaches to the two-scale convergence.(English)Zbl 1099.35012

Summary: Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definition by G. Nguetseng and G. Allaire two alternative definitions are introduced and compared. They enable us to weaken requirements on the admissibility of test functions $$\psi (x,y)$$. Properties and examples are added.

### MSC:

 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 74Q05 Homogenization in equilibrium problems of solid mechanics 76M50 Homogenization applied to problems in fluid mechanics

### Keywords:

two-scale convergence; weak convergence; homogenization
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### References:

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