Two-scale div-curl lemma
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 2, p. 291-321
The div-curl lemma, one of the basic results of the theory of compensated compactness of Murat and Tartar, does not take over to the case in which the two factors two-scale converge in the sense of Nguetseng. A suitable modification of the differential operators however allows for this extension. The argument follows the lines of a well-known paper of F. Murat of 1978, and uses a two-scale extension of the Fourier transform. This result is also extended to time-dependent functions, and is applied to a two-scale formulation of the Maxwell system of electromagnetism, that accounts for the energy embedded in both coarse- and fine-scale oscillations.
Classification:  35B27,  35J20,  74Q
@article{ASNSP_2007_5_6_2_291_0,
     author = {Visintin, Augusto},
     title = {Two-scale div-curl lemma},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {2},
     year = {2007},
     pages = {291-321},
     zbl = {1184.35040},
     mrnumber = {2352520},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2007_5_6_2_291_0}
}
Visintin, Augusto. Two-scale div-curl lemma. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 2, pp. 291-321. http://www.numdam.org/item/ASNSP_2007_5_6_2_291_0/

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