### Abstract

This paper considers the fundamental questions, such as existence and uniqueness, of a mathematical model arising in the MREIT system, which is an electrical impedance tomography technique integrated with magnetic resonance imaging. The mathematical model for MREIT is the Neumann problem of a nonlinear elliptic partial differential equation ∇ · (a(x)/|∇u(x)| ∇u(x)) = 0. We show that this Neumann problem belongs to one of two cases: either infinitely many solutions exist or no solution exists. This explains rigorously the reason why we have used the modified model in [O. Kwon, E. J. Woo, J. R. Yoon, and J. K. Seo, IEEE Trans. Biomed. Engrg., 49 (2002), pp. 160-167], which is a system of the Neumann problem associated with two different Neumann data. For this modified system, we prove a uniqueness result on the edge detection of a piecewise continuous conductivity distribution.

Original language | English |
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Pages (from-to) | 511-526 |

Number of pages | 16 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 34 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2003 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Mathematical Analysis*,

*34*(3), 511-526. https://doi.org/10.1137/S0036141001391354