Localized potentials in electrical impedance tomography

In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of adomain and low energy on another. We show that such potentials exist for general L^∞₊-conductivities inalmost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability resultfor the famous Calderón problem with partial data. We also show how to construct such potentials numericallyand use a connection with the factorization method to derive a new non-iterative algorithm forthe detection of inclusions in electrical impedance tomography.