Inverse conductivity problem with one measurement: Uniqueness of balls in R3

Hyeonbae Kang, Jin Keun Seo

Research output: Contribution to journalArticle

30 Citations (Scopus)


The location and size of an unknown ball D, entering the conductivity equation div ((1+(k-1)χD)▽u) = 0 in a bounded domain Ω⊂R3 are proven to be uniquely determined by any single non-zero Cauchy data (u, ∂u/∂ν) on ∂Ω. The global uniqueness results are obtained when D is restricted to be a convex polyhedron in three-dimensional space, and polygons and disks in the plane. The uniqueness of balls in three-dimensional space is presented.

Original languageEnglish
Pages (from-to)1533-1539
Number of pages7
JournalSIAM Journal on Applied Mathematics
Issue number5
Publication statusPublished - 1999 Jan 1


All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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