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.
Author(s): Habib Ammari, Hyeonbae Kang (auth.)
Series: Lecture Notes in Mathematics 1846
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2004
Language: English
Pages: 242
City: Berlin; New York
Tags: Partial Differential Equations
1. Introduction....Pages 1-4
Part I: Detection of Small Conductivity Inclusions....Pages 5-9
2. Transmission Problem....Pages 11-39
3. Generalized Polarization Tensors....Pages 41-64
4. Derivation of the Full Asymptotic Formula....Pages 65-78
5. Detection of Inclusions....Pages 79-101
Part II: Detection of Small Elastic Inclusions....Pages 103-107
6. Transmission Problem for Elastostatics....Pages 109-127
7. Elastic Moment Tensor....Pages 129-149
8. Derivation of Full Asymptotic Expansions....Pages 151-157
9. Detection of Inclusions....Pages 159-173
Part III: Detection of Small Electromagnetic Inclusions....Pages 175-178
10. Well-Posedness....Pages 179-183
11. Representation of Solutions....Pages 185-195
12. Derivation of Asymptotic Formulae....Pages 197-205
13. Reconstruction Algorithms....Pages 207-214
A. Appendices....Pages 215-221
References....Pages 223-236
Index....Pages 237-238
