Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems

Released on by Mourad Choulli
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  • Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems Book Detail

  • Author : Mourad Choulli
  • Release Date : 2016-06-03
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 88
  • ISBN 13 : 3319336428
  • File Size : 91,91 MB
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Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems by Mourad Choulli PDF Summary

Book Description: This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.

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Carleman Inequalities

Carleman Inequalities

File Size : 85,85 MB
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Over the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inve

Inverse Problems and Related Topics

Inverse Problems and Related Topics

File Size : 36,36 MB
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This volume contains 13 chapters, which are extended versions of the presentations at International Conference on Inverse Problems at Fudan University, Shanghai