Detection of Mines by Electric Measurements

In a homogeneous region Ω of earth with conductivity 1 a mine is possibly buried, occupying a region D and having conductivity ≠ 1; D is unknown, but meas ( D ) c > 0. We let electric current enter Ω at some point of ∂ Ω and exit it at another point of ∂ Ω, and we measure the resulting potential at some open portion of ∂ Ω. It is proved that if the error in the measurements is small enough, then one can assert whether or not a mine D is in fact buried in Ω. Some results on the location of D are also given.