We will show in three dimensions that if we know the
Dirichlet-to-Neumann map associated to the Schroedinger equation with a
potential around the intersection of a sphere centered outside the convex
hull of a bounded domain with smooth boundary, then we can determine uniquely the corresponding spherical mean of the potential with an appropriate measure. This allows to determine the potential near the boundary where the Dirichlet-to-Neumann map is measured. Similar results
are valid for Electrical Impedance Tomography.
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