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Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems

  • Mourad Choulli

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

About this book

Introduction

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.

Keywords

Carleman inequalities Elliptic equations Cauchy problems Inverse problems Stability

Authors and affiliations

  • Mourad Choulli
    • 1
  1. 1.Deptartment of MathematicsUniversity of LorraineMetzFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-33642-8
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-33641-1
  • Online ISBN 978-3-319-33642-8
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site