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In this paper, we derive a Sampling Method to solve the inverse shape problemof recovering an inclusion with a generalized impedance condition fromelectrostatic Cauchy data. The generalized impedance condition is asecond-order differential operator applied to the boundary of the inclusion. Weassume that the Dirichlet-to-Neumann mapping is given from measuring thecurrent on the outer boundary from an imposed voltage. A simple numericalexample is given to show the effectiveness of the proposed inversion method forrecovering the inclusion. We also consider the inverse impedance problem ofdetermining the material parameters from the Dirichlet-to-Neumann mappingassuming the inclusion has been reconstructed where uniqueness for thereconstruction of the coefficients is proven.

Detecting inclusions with a generalized impedance condition from electrostatic data via sampling