Lipschitz stability for the electrical impedance tomography problem: the complex case.

In this article we investigate the boundary value problem {div (gamma del u) = 0 in Omega {u= f on partial derivative Omega, where gamma is a complex valued L(infinity) coefficient, satisfying a strong ellipticity condition. In electrical impedance tomography, gamma represents the admittance of a conducting body. An interesting issue is the one of determining gamma uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map Lambda(gamma). Under the above general assumptions this problem is an open issue. In this article we prove that, if we assume a priori that gamma is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of gamma from Lambda(gamma) holds.