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Who came up with the idea of solving elliptic equations with periodic potentials and from there solving elliptic equations with asymptotically periodic potentials? I heard it was Pierre Louis Lions, but I found no records.

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    $\begingroup$ Are you referring to the method of asymptotic homogenization? It was developed by Lions and his students, among others, see e.g. Asymptotic Analysis for Periodic Structures (1978) by Bensoussan, Lions, and Papanicolaou. $\endgroup$
    – Conifold
    Aug 11, 2019 at 22:48
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    $\begingroup$ Could you give references for this method in your question please ? $\endgroup$
    – J.A
    Aug 12, 2019 at 11:22
  • $\begingroup$ For example in the Tang's paper: hindawi.com/journals/aaa/2014/607078 $\endgroup$
    – Pádua
    Aug 12, 2019 at 23:08
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    $\begingroup$ This paper explicitly references Lions's paper on the concentration compactness principle. $\endgroup$
    – Conifold
    Aug 13, 2019 at 0:33
  • $\begingroup$ Conifold, but in this Lions paper I did not find him dealing with periodic and asymptotically periodic cases. $\endgroup$
    – Pádua
    Aug 13, 2019 at 13:32

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