Local uniqueness in the inverse conductivity problem with one measurement
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- by G. Alessandrini, V. Isakov and J. Powell
- Trans. Amer. Math. Soc. 347 (1995), 3031-3041
- DOI: https://doi.org/10.1090/S0002-9947-1995-1303113-8
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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 $\partial \Omega$.References
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Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 3031-3041
- MSC: Primary 35R30; Secondary 31A25, 86A22
- DOI: https://doi.org/10.1090/S0002-9947-1995-1303113-8
- MathSciNet review: 1303113