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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.
@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},
pages = {291--321},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 6},
number = {2},
year = {2007},
mrnumber = {2352520},
zbl = {1184.35040},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_2_291_0/}
}
TY - JOUR AU - Visintin, Augusto TI - Two-scale div-curl lemma JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 291 EP - 321 VL - 6 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_2_291_0/ LA - en ID - ASNSP_2007_5_6_2_291_0 ER -
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://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_2_291_0/