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Transactions of the American Mathematical Society

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Local uniqueness in the inverse conductivity problem with one measurement

Authors: G. Alessandrini, V. Isakov and J. Powell
Journal: Trans. Amer. Math. Soc. 347 (1995), 3031-3041
MSC: Primary 35R30; Secondary 31A25, 86A22
MathSciNet review: 1303113
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Abstract: We prove local uniqueness of a domain $ D$ entering the conductivity equation $ {\text{div}}((1 + \chi (D))\nabla u) = 0$ in a bounded planar domain $ \Omega $ given the Cauchy data for $ u$ on a part of $ \partial \Omega $. The main assumption is that $ \nabla u$ has zero index on $ \partial \Omega $ which is easy to guarantee by choosing special boundary data for $ u$. To achieve our goals we study index of critical points of $ u$ on $ \partial \Omega $.

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