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A uniqueness theorem for an inverse boundary value problem in electrical prospection
Author(s) -
Sylvester John,
Uhlmann Gunther
Publication year - 1986
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160390106
Subject(s) - mathematics , uniqueness , mathematical analysis , boundary value problem , operator (biology) , constant (computer programming) , uniqueness theorem for poisson's equation , dirichlet distribution , inverse problem , elliptic boundary value problem , state (computer science) , dirichlet problem , dirichlet boundary condition , inverse , boundary (topology) , mixed boundary condition , geometry , algorithm , biochemistry , chemistry , repressor , computer science , transcription factor , gene , programming language
We show that a near constant conductivity of a two‐dimensional body can be uniquely determined by steady state direct current measurements at the boundary. Mathematically, we show that the coefficient γ in the operator ∇.γ∇ is uniquely determined by its Dirichlet integrals.