Detection of Mines by Electric Measurements

In a homogeneous region $\Omega $ of earth with conductivity 1 a mine is possibly buried, occupying a region D and having conductivity $ \ne 1$; D is unknown, but meas $( D )\geqq c > 0$. We let electric current enter $\Omega $ at some point of $\partial \Omega $ and exit it at another point of $\partial \Omega $, and we measure the resulting potential at some open portion of $\partial \Omega $. 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 $\Omega $. Some results on the location of D are also given.