Mathematics – Spectral Theory
Scientific paper
2010-12-21
Mathematics
Spectral Theory
to appear in Comm. Partial Differential Equations
Scientific paper
A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. 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.
Behrndt Jussi
Rohleder Jonathan
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