Inverse Problems and Imaging (IPI)

On uniqueness in the inverse conductivity problem with local data

Pages: 95 - 105, Volume 1, Issue 1, February 2007      doi:10.3934/ipi.2007.1.95

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Victor Isakov - Wichita State University, 1845 Fairmount, Wichita, KS, 67260-0033, United States (email)

Abstract: We show that the Dirichlet-to-Neumann map given on an arbitrary part of the boundary of a three-dimensional domain with zero Dirichlet (or Neumann) data on the remaining (spherical or plane) part of the boundary uniquely determines conductivity or potential coefficients. This is the first uniqueness result for the Calderon problem with zero data on unaccessible part of the boundary. Proofs use some modification of the method of complex geometrical solutions due to Calderon-Sylvester-Uhlmann.

Keywords:  Inverse Problems; Inverse Scattering Problems.
Mathematics Subject Classification:  Primary: 35R30; Secondary: 78A46.

Received: June 2006;      Available Online: January 2007.