Cloaking using complementary media in the quasistatic regime
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1509-1518.

Cloaking using complementary media was suggested by Lai et al. in [8]. The study of this problem faces two difficulties. Firstly, this problem is unstable since the equations describing the phenomenon have sign changing coefficients, hence the ellipticity is lost. Secondly, the localized resonance, i.e., the field explodes in some regions and remains bounded in some others as the loss goes to 0, might appear. In this paper, we give a proof of cloaking using complementary media for a class of schemes inspired from [8] in the quasistatic regime. To handle the localized resonance, we introduce the technique of removing localized singularity and apply a three spheres inequality. The proof also uses the reflecting technique in [11]. To our knowledge, this work presents the first proof on cloaking using complementary media.

DOI : 10.1016/j.anihpc.2015.06.004
Classification : 35B34, 35B35, 35B40, 35J05, 78A25, 78M35
Mots-clés : Negative index materials, Cloaking, Sign changing coefficients, Localized resonance, Complementary media 
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Nguyen, Hoai-Minh. Cloaking using complementary media in the quasistatic regime. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1509-1518. doi : 10.1016/j.anihpc.2015.06.004. http://www.numdam.org/articles/10.1016/j.anihpc.2015.06.004/

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