Lipschitz Stability for the Electrical Impedance Tomography Problem: The Complex Case

Abstract

In this article we investigate the boundary value problem where γ is a complex valued L ∞ coefficient, satisfying a strong ellipticity condition. In electrical impedance tomography, γ represents the admittance of a conducting body. An interesting issue is the one of determining γ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map Λγ. Under the above general assumptions this problem is an open issue. In this article we prove that, if we assume a priori that γ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of γ from Λγ holds.