The layer potential technique for the inverse conductivity problem

Hyeonbae Kang, Jin Keun Seo

Research output: Contribution to journalArticle

79 Citations (Scopus)

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 Rn (n ≥ 3) with one measurement corresponding to a certain Neumann data.

Original languageEnglish
Pages (from-to)267-278
Number of pages12
JournalInverse Problems
Volume12
Issue number3
DOIs
Publication statusPublished - 1996 Jun 1

All Science Journal Classification (ASJC) codes

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

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