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On uniqueness in the inverse conductivity problem
Author(s) -
Sever Ali
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199908)22:12<953::aid-mma10>3.0.co;2-j
Subject(s) - mathematics , uniqueness , lipschitz continuity , dirichlet distribution , mathematical analysis , boundary (topology) , inverse problem , inverse , elliptic curve , boundary value problem , dirichlet problem , geometry
We derive a uniqueness proof of inclusions of different (analytic) conductivities in the equation div( a grad u ) = 0 in Ω under the minimal assumptions: (i) the boundaries of inclusions are only Lipschitz and (ii) we have no topological assumptions. For any Dirichlet data g , we are given the Neumann data h ; in other words, results of all possible boundary measurements are known. For this purpose, we use and modify the construction of singular solution of elliptic equations due to Alessandrini [1]. Copyright © 1999 John Wiley & Sons, Ltd.