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

Abstract

For the two dimensional Schrödinger equation in a bounded domain, we prove uniqueness of determination of potentials in $W_p^1(\Omega ),p>2$ in the case where we apply all possible Neumann data supported on an arbitrarily non-empty open set $\tilde{\Gamma }$ of the boundary and observe the corresponding Dirichlet data on $\tilde{\Gamma }$. An immediate consequence is that one can uniquely determine a conductivity in $W_p^3(\Omega )$ with $p>2$ by measuring the voltage on an open subset of the boundary corresponding to current supported in the same set.

13 pages

References in corpus (3)

• The inverse problem of the Schrödinger equation in the plane; A dissection of Bukhgeim's result
• Partial Cauchy Data for General Second-Order Elliptic Operators in Two Dimensions
• Inverse Boundary Problems for Systems in Two Dimensions

Cited by in corpus (1)

• Uniqueness for inverse boundary value problems by Dirichlet-to -Neumann map on subboundaries