Abstract
We consider the recovery of piecewise constant conductivity and an unknown inner core in inverse conductivity problem. We first show the unique recovery of the conductivity in a one layer structure without inner core by one measurement on any surface enclosing the unknown medium. Then we recover the unknown inner core in a one layer structure. We then show that in a two layer structure, the conductivity can be uniquely recovered by using one measurement.
Highlights
The function h is a harmonic function in Rd representing the background electrical potential, and u represents the perturbed electrical potential
We first prove that the conductivity in a one layer structure without inner core can be recovered by using one measurement
As we have mentioned that SB is defined on R3 \ ∂B, and is continuous across ∂B, we shall still use SB[φ] to denote for the trace of SB[φ] on ∂B
Summary
School of Mathematics and Statistics, Hunan University of Commerce School of Mathematics and Statistics, Central South University Changsha, Hunan, China School of Mathematics and Statistics, Central South University Changsha, Hunan, China (Communicated by Hongyu Liu)
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