# A NOTE ON UNIQUENESS AND STABILITY FOR THE INVERSE CONDUCTIVITY PROBLEM WITH ONE MEASUREMENT

• Kang, Hyeon-Bae (Department of Mathematics, Seoul National University) ;
• Seo, Jin-Keun (Department of Mathematics, Yonsei University)
• Published : 2001.07.01
• 61 3

#### Abstract

We consider the inverse conductivity problem to identify the unknown conductivity $textsc{k}$ as well as the domain D. We show hat, unlike the case when $textsc{k}$ is known, even a two or three dimensional ball may not be identified uniquely if the conductivity constant $textsc{k}$ is not known. We find a necessary and sufficient condition on the Cauchy data (u│∂Ω, g) for the uniqueness in identification of $textsc{k}$ and D. We also discuss on failure of stability.

#### Keywords

inverse conductivity problem;non-uniqueness;Layer potentials

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