Inverse conductivity problem with one measurement: Error estimates and approximate identification for perturbed disks

Eugene Fabes, Hyeonbae Kang, Jin Keun Seo

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21 Citations (Scopus)

Abstract

This paper studies the global uniqueness and stability questions of the inverse conductivity problem to determine the unknown object D entering div((1 + (k - 1)XD)∇u) = 0 in Ω and ∂u/∂v = g on ∂Ω from the boundary measurement ∧(g) = u|∂Ω. The results of this paper are fourfold. We first obtain a Hölder stability estimate for disks. Second, a uniform stability estimate for the direct problem is obtained. Third, we obtain the stability estimates \D\ \D̄2| + |D2 \D̄1| ≤ C(∥∧D1(g) - ∧D2(g)∥αL(∂Ω) + ∈) for some α > 0 when g satisfies some condition if D1 and D2 are ∈-perturbations of two disks. We then drop the condition on g and show that if ∧D1 (g) = ∧D2 (g) on ∂Ω, then the two domains must be very close.

Original languageEnglish
Pages (from-to)699-720
Number of pages22
JournalSIAM Journal on Mathematical Analysis
Volume30
Issue number4
DOIs
Publication statusPublished - 1999 Jan 1

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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