Inequalities for inverse scattering problems in absorbing media

In this paper we derive two inequalities concerning two two-dimensional scattering problems: in the first one the infinite cylinder is an obstacle and the electric field satisfies an impedance boundary condition while in the second one the scatterer is inhomogeneous. When the impedance and the refractive index are two known constants these two inequalities can be used to obtain lower bounds on the size of the scatterer. By means of some numerical applications for the impedance problem, we show that the corresponding lower bound is reliable both in the case of full-aperture data and in the case of scattering from a limited aperture.