Kim, SungwhanKwon, OhinSeo, Jin KeunYoon, Jeong-Rock2007-08-162007-08-162001-07https://hdl.handle.net/11299/3666This paper considers the fundamental questions, such as existence and uniqueness, of a mathematical model arising in MREIT system, which is 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 $\div\left(\frac{a(x)}{|\na u(x)|}\na u(x)\right)=0$. We show that this Neumann problem belongs to one of two cases: either infinitely many solutions or no solution exist. This explains rigorously the reason why we have used the modified model in [7] 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.