On the uniqueness of inverse problems from incomplete boundary data

We present a generalization of our previous results on the uniqueness of inverse coefficient problems for elliptic equations. The theorem proved here is formulated for piecewise-constant coefficients with piecewise smooth interfaces of discontinuities which require local boundary data. We consider problems with coefficients unknown at one side as well as at both sides of the boundary. The uniqueness of the former is proven; the latter can yield up to two solutions. The proofs are based on a simple analysis of singularities of the Green functions. The presented approach exactly conforms to some important inverse problems arising in applications of electromagnetic geophysics.