Direct reconstruction of anisotropic self-adjoint inclusions in the Calderón problem

We extend the monotonicity method for direct exact reconstruction of inclusions in the partial data Calderón problem, to the case of anisotropic conductivities in any spatial dimension d≥ 2. Specifically, from a local Neumann-to-Dirichlet map, we give reconstruction methods of inclusions based on unknown anisotropic self-adjoint perturbations to a known anisotropic conductivity coefficient. A main assumption is a definiteness condition for the perturbations near the outer inclusion boundaries. This additionally provides new insights into the non-uniqueness issues of the anisotropic Calderón problem.