On quasi-static cloaking due to anomalous localized resonance in $\mathbb{R}^3$

This work concerns the cloaking due to anomalous localized resonance (CALR) in the quasi-static regime. We extend the related two-dimensional studies in [2,10] to the three-dimensional setting. CALR is shown not to take place for the plasmonic configuration considered in [2,10] in the three-dimensional case. We give two different constructions which ensure the occurrence of CALR. There may be no core or an arbitrary shape core for the cloaking device. If there is a core, then the dielectric distribution inside it could be arbitrary.