Reconstruction of inclusions for the inverse boundary value problem with mixed type boundary condition and source term

Abstract

We considered identifying the shape of an unknown inclusion inside an anisotropic conductive medium. The assumption for the regularity of the background conductivity is that which guarantees the weak unique continuation property and that of the inclusion is just bounded measurable. Under this assumption for the conductivity, we adapted the probe method to give a reconstruction formula for identifying the shape of inclusion. In particular, we introduced a new method for estimating the reflected solution which is one of the major ingredients of the probe method.