An Inverse Problem of Calderon Type with Partial Data

作者：Behrndt Jussi^*; Rohleder Jonathan

来源：Communications in Partial Differential Equations, 2012, 37(6): 1141-1159.

DOI：10.1080/03605302.2011.632464

• Calderon problem
• Dirichlet-to-Neumann map
• Gelfand problem
• Elliptic differential Operator
• Partial data.

A generalized variant of the Calderon problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension n = 2. The following two results are shown: (i) The selfadjoint Dirichlet operator associated with an elliptic differential expression on a bounded Lipschitz domain is determined uniquely up to unitary equivalence by the knowledge of the Dirichlet-to-Neumann map on an open subset of the boundary, and (ii) the Dirichlet operator can be reconstructed from the residuals of the Dirichlet-to-Neumann map on this subset.

• 出版日期2012