  In this paper, we derive a Sampling Method to solve the inverse shape problem
of recovering an inclusion with a generalized impedance condition from
electrostatic Cauchy data. The generalized impedance condition is a
second-order differential operator applied to the boundary of the inclusion. We
assume that the Dirichlet-to-Neumann mapping is given from measuring the
current on the outer boundary from an imposed voltage. A simple numerical
example is given to show the effectiveness of the proposed inversion method for
recovering the inclusion. We also consider the inverse impedance problem of
determining the material parameters from the Dirichlet-to-Neumann mapping
assuming the inclusion has been reconstructed where uniqueness for the
reconstruction of the coefficients is proven.
