The aim of this paper is twofold. First, we derive quantitative uniqueness estimates in the form of three-ball inequalities for solutions of complex conductivity equations whose leading coefficients are Lipschitz. Second, we study the problem of estimating the size of an inclusion embedded inside a conductive body with anisotropic complex admittivity by one boundary measurement. Practical motivations for studying such inverse problems are also given.


  1. Carleman estimate
  2. three-ball inequalities
  3. size estimate

MSC codes

  1. 35R30
  2. 35R25
  3. 35B60

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Information & Authors


Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 570 - 580
ISSN (online): 1095-7154


Submitted: 5 November 2018
Accepted: 5 November 2019
Published online: 12 February 2020


  1. Carleman estimate
  2. three-ball inequalities
  3. size estimate

MSC codes

  1. 35R30
  2. 35R25
  3. 35B60



Cătălin I. Cârstea

Funding Information

Ministry of Science and Technology https://doi.org/10.13039/100007225 : 105-2115-M-002-014-MY3
National Foundation for Science and Technology Development https://doi.org/10.13039/100007224 : 101.02-2015.21

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