Stability of the recovery of surface impedances in inverse scattering (Q1283003)

The author considers an inverse problem arising in scattering theory, which is for determining the surface impedance on the boundary of a known obstacle from knowledge of the far field pattern for the scattering of incident time-harmonic plane wave. It is well known that the above problem has a unique solution, but is ill posed. The author shows that the inverse problem is well posed provided that the surface impedance has an upper bound in the \(C^{1+\eta}\) norm.