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 '19 at 22:48
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    $\begingroup$ Could you give references for this method in your question please ? $\endgroup$ – J.A Aug 12 '19 at 11:22
  • $\begingroup$ For example in the Tang's paper: hindawi.com/journals/aaa/2014/607078 $\endgroup$ – Pádua Aug 12 '19 at 23:08
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    $\begingroup$ This paper explicitly references Lions's paper on the concentration compactness principle. $\endgroup$ – Conifold Aug 13 '19 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 '19 at 13:32

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