Kohn, R. V.; Shen, H.; Vogelius, M. S.; Weinstein, M. I. Cloaking via change of variables in electric impedance tomography. (English) Zbl 1153.35406 Inverse Probl. 24, No. 1, Article ID 015016, 21 p. (2008). Summary: A recent paper by Pendry et al. [Science 312, 1780–1782 (2006)] used the coordinate invariance of Maxwell’s equations to show how a region of space can be ‘cloaked’-in other words, made inaccessible to electromagnetic sensing-by surrounding it with a suitable (anisotropic and heterogeneous) dielectric shield. Essentially the same observation was made several years earlier by A. Greenleaf, M. Lassas and G. Uhlmann [Math. Res. Lett. 10, No. 5–6, 685–693 (2003; Zbl 1054.35127)] in the closely related setting of electric impedance tomography. These papers, though brilliant, have two shortcomings: (a) the cloaks they consider are rather singular; and (b) the analysis by Greenleaf, Lassas and Uhlmann does not apply in space dimension \(n = 2\). The present paper provides a fresh treatment that remedies these shortcomings in the context of electric impedance tomography. In particular, we show how a regular near-cloak can be obtained using a nonsingular change of variables, and we prove that the change-of-variable-based scheme achieves perfect cloaking in any dimension \(n \geq 2\). Cited in 5 ReviewsCited in 65 Documents MSC: 35R30 Inverse problems for PDEs 35Q60 PDEs in connection with optics and electromagnetic theory 78A25 Electromagnetic theory (general) 92C55 Biomedical imaging and signal processing Keywords:Maxwell’s equations; electric impedance tomography; cloaking Citations:Zbl 1054.35127 PDFBibTeX XMLCite \textit{R. V. Kohn} et al., Inverse Probl. 24, No. 1, Article ID 015016, 21 p. (2008; Zbl 1153.35406) Full Text: DOI