Non-uniqueness results for the Calderon inverse problem with local or disjoint data
Niky Kamran - McGill University
The anisotropic Calderon inverse problem consists in recovering the metric of a compact connected Riemannian manifold with boundary from the knowledge of the Dirichlet-to-Neumann map at fixed energy. A fundamental result due to Lee and Uhlmann states that there is uniqueness in the analytic case. We shall present counterexamples to uniqueness in cases when:
1) The metric smooth in the interior of the manifold, but only H\"older continuous on one connected component of the boundary, with the Dirichlet and Neumann data being measured on the same proper subset of the boundary.
2) The metric is smooth everywhere and Dirichlet and Neumann data are measured on disjoint subsets of the boundary.
This is joint work with Thierry Daude (Cergy-Pontoise) and Francois Nicoleau (Nantes).