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Mathematics > Analysis of PDEs

arXiv:1810.00576 (math)
[Submitted on 1 Oct 2018]

Title:Uniqueness estimates for the general complex conductivity equation and their applications to inverse problems

Authors:Catalin Carstea, Tu Nguyen, Jenn-Nan Wang
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Abstract:The aim of the paper is twofold. Firstly, we would like to derive quantitative uniqueness estimates for solutions of the general complex conductivity equation. It is still unknown whether the \emph{strong} unique continuation property holds for such equations. Nonetheless, in this paper, we show that the unique continuation property in the form of three-ball inequalities is satisfied for the complex conductivity equation under only Lipschitz assumption on the leading coefficients. The derivation of such estimates relies on a delicate Carleman estimate. Secondly, we study the problem of estimating the size of an inclusion embedded inside of a conductive body with anisotropic complex admittivity by one boundary measurement. The study of such inverse problem is motivated by practical problems.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1810.00576 [math.AP]
  (or arXiv:1810.00576v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1810.00576

Submission history

From: Jenn-Nan Wang [view email]
[v1] Mon, 1 Oct 2018 08:30:18 UTC (13 KB)
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