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Open issues of stability for the inverse conductivity problem. (English) Zbl 1221.35443

The paper deals with the inverse conductivity problem consisting of finding the conductivity being a bounded measured function in a bounded connected open set in \(\mathbb{R}^n\), \(n\geq 2\) from the given Dirichlet-to-Neumann operator. The author studies minimal a priori assumptions on the regularity of the conductivity providing uniqueness of the reconstruction, a variant of the inverse problem where only a part of the boundary is involved in the known Dirichlet and Neumann data. The possibility of using different kinds of a priory information in order to improve the stability of the reconstruction is discussed.

MSC:

35R30 Inverse problems for PDEs
35R25 Ill-posed problems for PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
35B35 Stability in context of PDEs
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