The Calderon problem for conormal potentials, I: Global uniqueness and reconstruction

Details The Calderon problem for conormal potentials, I: Global uniqueness and reconstruction The Calderon problem for conormal potentials, I: Global uniqueness and reconstruction

2001-12-12

arxiv.org/abs/math/0112130v2

Mathematics

Analysis of PDEs

Final revision with corrections; 23 pages; to appear in Comm. Pure Appl. Math

Scientific paper

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.

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