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

In this paper we investigate the boundary value problem ${div(γ\nabla u)=0 in Ω, u=f on \partialΩ$ where $γ$ is a complex valued $L^\infty$ 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 $Λ_γ$. Under the above general assumptions this problem is an open issue. In this paper 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 $Λ_γ$ holds.

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