## 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)∥^{α}_{L}∞ _{(∂Ω)} + ∈) for some α > 0 when g satisfies some condition if D_{1} and D_{2} 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 language | English |
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Pages (from-to) | 699-720 |

Number of pages | 22 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 30 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1999 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics