Examples of exponential instability for inverse inclusion and scattering problems

Abstract

Following a recent paper by Mandache (2001 Inverse Problems 17 1435–44), we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to an elliptic inverse problem concerning the determination of inclusions in a conductor by different kinds of boundary measurements and to inverse obstacle acoustic scattering problems and we show that these problems are exponentially ill-posed.