Reconstruction of Small Inhomogeneities from Boundary Measurements

1. Front Matter

   Pages N2-IX

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2. 1. Introduction

   • Habib Ammari, Hyeonbae Kang

   Pages 1-4

3. Part I: Detection of Small Conductivity Inclusions

   • Habib Ammari, Hyeonbae Kang

   Pages 6-9

4. 2. Transmission Problem

   • Habib Ammari, Hyeonbae Kang

   Pages 11-39

5. 3. Generalized Polarization Tensors

   • Habib Ammari, Hyeonbae Kang

   Pages 41-64

6. 4. Derivation of the Full Asymptotic Formula

   • Habib Ammari, Hyeonbae Kang

   Pages 65-78

7. 5. Detection of Inclusions

   • Habib Ammari, Hyeonbae Kang

   Pages 79-101

8. Part II: Detection of Small Elastic Inclusions

   • Habib Ammari, Hyeonbae Kang

   Pages 104-107

9. 6. Transmission Problem for Elastostatics

   • Habib Ammari, Hyeonbae Kang

   Pages 109-127

10. 7. Elastic Moment Tensor

    • Habib Ammari, Hyeonbae Kang

    Pages 129-149

11. 8. Derivation of Full Asymptotic Expansions

    • Habib Ammari, Hyeonbae Kang

    Pages 151-157

12. 9. Detection of Inclusions

    • Habib Ammari, Hyeonbae Kang

    Pages 159-173

13. Part III: Detection of Small Electromagnetic Inclusions

    • Habib Ammari, Hyeonbae Kang

    Pages 176-178

14. 10. Well-Posedness

    • Habib Ammari, Hyeonbae Kang

    Pages 179-183

15. 11. Representation of Solutions

    • Habib Ammari, Hyeonbae Kang

    Pages 185-195

16. 12. Derivation of Asymptotic Formulae

    • Habib Ammari, Hyeonbae Kang

    Pages 197-205

17. 13. Reconstruction Algorithms

    • Habib Ammari, Hyeonbae Kang

    Pages 207-214

18. A. Appendices

    • Habib Ammari, Hyeonbae Kang

    Pages 215-221

19. References

    • Habib Ammari, Hyeonbae Kang

    Pages 223-236

20. Index

    • Habib Ammari, Hyeonbae Kang

    Pages 237-238

This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.

• Helmholtz equation
• inverse boundary value problems
• layer potential techniques
• partial differential equation
• reconstruction
• small inhomogeneities
• partial differential equations

From the reviews:

"The book … describes a ‘fresh and promising techniques for the reconstruction of small inclusions from boundary measurements’ and the presentation is ‘intended to be self-contained’. … The problems discussed in the book are of interest both theoretically and practically. This book hopefully will stimulate the research in the area of finding small inhomogeneities from experimental data." (Alexander G. Ramm, Zentralblatt MATH, Vol. 1113 (15), 2007)

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