Thin cylindrical conductivity inclusions in a 3-dimensional domain: polarization tensor and unique determination from boundary data

Elena Beretta (1) , Yves Capdeboscq (2) , Elisa Francini (3)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
2 MI - Mathematical Institute [Oxford]
3 Dipartimento di Matematica "Ulisse Dini"

We consider a $3$-dimensional conductor containing an inclusion that can be repr esented as a cylinder with fixed axis and a small basis. As the size of the bas is of the cylinder approaches zero, the voltage perturbation can be described by means of a polarization tensor. We give an explicit characterization of the pol arization tensor of cylindrical inclusions in terms of the polarization tensor o f its base, and we use this result to show that the axis of the inclusion can b e uniquely determined by boundary values of the voltage perturbation.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Elena Beretta, Yves Capdeboscq, Elisa Francini. Thin cylindrical conductivity inclusions in a 3-dimensional domain: polarization tensor and unique determination from boundary data. Inverse Problems, 2009, 25, pp.065004. ⟨10.1088/0266-5611/25/6/065004⟩. ⟨hal-00342730⟩