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Browsing by Author "Kim, Sungwhan"

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    On a nonlinear partial differential equation arising in Magnetic Resonance Electrical Impedance Tomography
    (2001-07) Kim, Sungwhan; Kwon, Ohin; Seo, Jin Keun; Yoon, Jeong-Rock
    This 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.