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Inverse Boundary Value Problem by Partial data for the Neumann-to-Dirichlet-map in two dimensions (1210.1255v1)

Published 3 Oct 2012 in math-ph and math.MP

Abstract: For the two dimensional Schr\"odinger equation in a bounded domain, we prove uniqueness of determination of potentials in $W1_p(\Omega),\,\, p>2$ in the case where we apply all possible Neumann data supported on an arbitrarily non-empty open set $\widetilde\Gamma$ of the boundary and observe the corresponding Dirichlet data on $\widetilde{\Gamma}$. An immediate consequence is that one can uniquely determine a conductivity in $W3_p(\Omega)$ with $p>2$ by measuring the voltage on an open subset of the boundary corresponding to current supported in the same set.

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