On uniqueness in the inverse conductivity problem with local data. (English) Zbl 1125.35113
Summary: 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.
MSC:
35R30 | Inverse problems for PDEs |
78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |