Allan Greenleaf, Matti Lassas, Gunther Uhlmann
Published 2001-12-12, updated 2002-10-04Version 2
In dimensions greater than or equal to three, we establish global uniqueness and obtain reconstruction in the Calderon problem for the Schrodinger equation with certain singular potentials. The potentials considered are conormal of order less than 1-k with respect to submanifolds (of arbitrary codimension k). This gives positive results for (conormal) conductivities which are Holder of any order > 1. A related problem for highly singular potentials is shown to exhibit nonuniqueness.
Comments: Final revision with corrections; 23 pages; to appear in Comm. Pure Appl. Math
On the scattering for the $\bar{\partial}$- equation and reconstruction of convection terms
Nachman's reconstruction for the Calderon problem with discontinuous conductivities
Reconstruction in the Calderon Problem with Partial Data
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