The location and size of an unknown ball D, entering the conductivity equation div ((1+(k-1)χD)▽u) = 0 in a bounded domain Ω⊂R3 are proven to be uniquely determined by any single non-zero Cauchy data (u, ∂u/∂ν) on ∂Ω. The global uniqueness results are obtained when D is restricted to be a convex polyhedron in three-dimensional space, and polygons and disks in the plane. The uniqueness of balls in three-dimensional space is presented.
All Science Journal Classification (ASJC) codes
- Applied Mathematics