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© 2004

Reconstruction of Small Inhomogeneities from Boundary Measurements

  • Authors
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1846)

Table of contents

  1. Front Matter
    Pages N2-IX
  2. Habib Ammari, Hyeonbae Kang
    Pages 1-4
  3. Habib Ammari, Hyeonbae Kang
    Pages 6-9
  4. Habib Ammari, Hyeonbae Kang
    Pages 11-39
  5. Habib Ammari, Hyeonbae Kang
    Pages 41-64
  6. Habib Ammari, Hyeonbae Kang
    Pages 65-78
  7. Habib Ammari, Hyeonbae Kang
    Pages 79-101
  8. Habib Ammari, Hyeonbae Kang
    Pages 104-107
  9. Habib Ammari, Hyeonbae Kang
    Pages 109-127
  10. Habib Ammari, Hyeonbae Kang
    Pages 129-149
  11. Habib Ammari, Hyeonbae Kang
    Pages 151-157
  12. Habib Ammari, Hyeonbae Kang
    Pages 159-173
  13. Habib Ammari, Hyeonbae Kang
    Pages 176-178
  14. Habib Ammari, Hyeonbae Kang
    Pages 179-183
  15. Habib Ammari, Hyeonbae Kang
    Pages 185-195
  16. Habib Ammari, Hyeonbae Kang
    Pages 197-205
  17. Habib Ammari, Hyeonbae Kang
    Pages 207-214
  18. Habib Ammari, Hyeonbae Kang
    Pages 215-221
  19. Habib Ammari, Hyeonbae Kang
    Pages 223-236
  20. Habib Ammari, Hyeonbae Kang
    Pages 237-238

About this book

Introduction

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.

Keywords

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

Bibliographic information

  • Book Title Reconstruction of Small Inhomogeneities from Boundary Measurements
  • Authors Habib Ammari
    Hyeonbae Kang
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title LNM
  • DOI https://doi.org/10.1007/b98245
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-22483-9
  • eBook ISBN 978-3-540-44501-2
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages X, 242
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Partial Differential Equations
  • Buy this book on publisher's site
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Reviews

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)