### Abstract

We consider the inverse conductivity problem for the equaiton div((1 + (k - 1)XD)▽α = 0 determining the unknown object D contained in a domian Ω with one measurement on ∂Ω The method in this paper is the layer potential technique. We find a representation formula for the solution to the equation using single layer potentials on D and Ω. Using this representation formula, we prove that the location and size of a disk D contained in a simply connected bounded Lipschitz domain Ω can be determined with one measurement corresponding to arbitreary non-zero Neumann data on ∂Ω (Previously, it was known that a disk can be determined with one measurement if Ω is assumed to be the half space.) We also prove a weaker version of the uniqueness for balls in R^{n} (n ≥ 3) with one measurement corresponding to a certain Neumann data.

Original language | English |
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Pages (from-to) | 267-278 |

Number of pages | 12 |

Journal | Inverse Problems |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1996 Jun 1 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics

### Cite this

*Inverse Problems*,

*12*(3), 267-278. https://doi.org/10.1088/0266-5611/12/3/007

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*Inverse Problems*, vol. 12, no. 3, pp. 267-278. https://doi.org/10.1088/0266-5611/12/3/007

**The layer potential technique for the inverse conductivity problem.** / Kang, Hyeonbae; Seo, Jin Keun.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The layer potential technique for the inverse conductivity problem

AU - Kang, Hyeonbae

AU - Seo, Jin Keun

PY - 1996/6/1

Y1 - 1996/6/1

N2 - We consider the inverse conductivity problem for the equaiton div((1 + (k - 1)XD)▽α = 0 determining the unknown object D contained in a domian Ω with one measurement on ∂Ω The method in this paper is the layer potential technique. We find a representation formula for the solution to the equation using single layer potentials on D and Ω. Using this representation formula, we prove that the location and size of a disk D contained in a simply connected bounded Lipschitz domain Ω can be determined with one measurement corresponding to arbitreary non-zero Neumann data on ∂Ω (Previously, it was known that a disk can be determined with one measurement if Ω is assumed to be the half space.) We also prove a weaker version of the uniqueness for balls in Rn (n ≥ 3) with one measurement corresponding to a certain Neumann data.

AB - We consider the inverse conductivity problem for the equaiton div((1 + (k - 1)XD)▽α = 0 determining the unknown object D contained in a domian Ω with one measurement on ∂Ω The method in this paper is the layer potential technique. We find a representation formula for the solution to the equation using single layer potentials on D and Ω. Using this representation formula, we prove that the location and size of a disk D contained in a simply connected bounded Lipschitz domain Ω can be determined with one measurement corresponding to arbitreary non-zero Neumann data on ∂Ω (Previously, it was known that a disk can be determined with one measurement if Ω is assumed to be the half space.) We also prove a weaker version of the uniqueness for balls in Rn (n ≥ 3) with one measurement corresponding to a certain Neumann data.

UR - http://www.scopus.com/inward/record.url?scp=0000369989&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000369989&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/12/3/007

DO - 10.1088/0266-5611/12/3/007

M3 - Article

VL - 12

SP - 267

EP - 278

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 3

ER -