On regularized full-and partial-cloaks in acoustic scattering

The aim of this work is to derive sharp quantitative estimates of the qualitative convergence results developed in [28] for regularized full- and partial-cloaks via the transformation-optics approach. Let Γ0 be a compact set in R3 and Γδ be a δ-neighborhood of Γ0 for δ∈R+. Γδ represents the virtual domain used for the blow-up construction. By incorporating suitably designed lossy layers, it is shown that if the generating set Γ0 is a generic curve, then one would have an approximate full-cloak within δ2 to the perfect full-cloak; whereas if Γ0 is the closure of an open subset on a flat surface, then one would have an approximate partial-cloak within δ to its perfect counterpart. The estimates derived are independent of the contents being cloaked; that is, the cloaking devices are capable of nearly cloaking an arbitrary content. Furthermore, as a significant byproduct, our argument allows the relaxation of the convexity requirement on Γ0 in [28], which is critical for the Mosco convergence argument therein.