Single-logarithmic stability for the Calder\'on problem with local data

We prove an optimal stability estimate for Electrical Impedance Tomography with local data, in the case when the conductivity is precisely known on a neighborhood of the boundary. The main novelty here is that we provide a rather general method which enables to obtain the H\"older dependence of a global Dirichlet to Neumann map from a local one on a larger domain when, in the layer between the two boundaries, the coefficient is known.Comment: 12 page

Cloaking due to anomalous localized resonance in plasmonic structures of confocal ellipses

If a core of dielectric material is coated by a plasmonic structure of negative dielectric material with non-zero loss parameter, then anomalous localized resonance may occur as the loss parameter tends to zero and the source outside the structure can be cloaked. It has been proved that the cloaking due to anomalous localized resonance (CALR) takes place for structures of concentric disks and the critical radius inside which the sources are cloaked has been computed. In this paper, it is proved that CALR takes place for structures of confocal ellipses and the critical elliptic radii are computed. The method of this paper uses the spectral analysis of the Neumann-Poincar\'e type operator associated with two interfaces (the boundaries of the core and the shell)

Bounds on the size of an inclusion using the translation method for two-dimensional complex conductivity

The size estimation problem in electrical impedance tomography is considered when the conductivity is a complex number and the body is two-dimensional. Upper and lower bounds on the volume fraction of the unknown inclusion embedded in the body are derived in terms of two pairs of voltage and current data measured on the boundary of the body. These bounds are derived using the translation method. We also provide numerical examples to show that these bounds are quite tight and stable under measurement noise.Comment: 15 pages, 5 figures, 5 table