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Layer Potential Techniques in Spectral Analysis
 
Habib Ammari Ecole Polytechnique, Palaiseau, France
Hyeonbae Kang Inha University, Incheon, South Korea
Hyundae Lee Inha University, Incheon, South Korea
Front Cover for Layer Potential Techniques in Spectral Analysis
Available Formats:
Hardcover ISBN: 978-0-8218-4784-8
Product Code: SURV/153
202 pp 
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN: 978-1-4704-1380-4
Product Code: SURV/153.E
202 pp 
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $117.00
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AMS Member Price: $93.60
Front Cover for Layer Potential Techniques in Spectral Analysis
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  • Front Cover for Layer Potential Techniques in Spectral Analysis
  • Back Cover for Layer Potential Techniques in Spectral Analysis
Layer Potential Techniques in Spectral Analysis
Habib Ammari Ecole Polytechnique, Palaiseau, France
Hyeonbae Kang Inha University, Incheon, South Korea
Hyundae Lee Inha University, Incheon, South Korea
Available Formats:
Hardcover ISBN:  978-0-8218-4784-8
Product Code:  SURV/153
202 pp 
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN:  978-1-4704-1380-4
Product Code:  SURV/153.E
202 pp 
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $117.00
MAA Member Price: $105.30
AMS Member Price: $93.60
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1532009
    MSC: Primary 47; 31; 34; 35; 45; 30;

    Since the early part of the twentieth century, the use of integral equations has developed into a range of tools for the study of partial differential equations. This includes the use of single- and double-layer potentials to treat classical boundary value problems.

    The aim of this book is to give a self-contained presentation of an asymptotic theory for eigenvalue problems using layer potential techniques with applications in the fields of inverse problems, band gap structures, and optimal design, in particular the optimal design of photonic and phononic crystals. Throughout this book, it is shown how powerful the layer potentials techniques are for solving not only boundary value problems but also eigenvalue problems if they are combined with the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. The general approach in this book is developed in detail for eigenvalue problems for the Laplacian and the Lamé system in the following two situations: one under variation of domains or boundary conditions and the other due to the presence of inclusions.

    The book will be of interest to researchers and graduate students working in the fields of partial differential equations, integral equations, and inverse problems. Researchers in engineering and physics may also find this book helpful.

    Readership

    Graduate students and research mathematicians interested in PDE's, integral equations, and spectral analysis.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Gohberg-Sigal theory
    • 1. Generalized argument principle and Rouché’s theorem
    • Eigenvalue perturbation problems and applications
    • 2. Layer potentials
    • 3. Eigenvalue perturbations of the Laplacian
    • 4. Vibration testing for detecting internal corrosion
    • 5. Perturbations of scattering frequencies of resonators with narrow slits and slots
    • 6. Eigenvalue perturbations of the Lamé system
    • Photonic and phononic band gaps and optimal design
    • 7. Floquet transform, spectra of periodic elliptic operators, and quasi-periodic layer potentials
    • 8. Photonic band gaps
    • 9. Phononic band gaps
    • 10. Optimal design problems
  • Request Review Copy
  • Get Permissions
Volume: 1532009
MSC: Primary 47; 31; 34; 35; 45; 30;

Since the early part of the twentieth century, the use of integral equations has developed into a range of tools for the study of partial differential equations. This includes the use of single- and double-layer potentials to treat classical boundary value problems.

The aim of this book is to give a self-contained presentation of an asymptotic theory for eigenvalue problems using layer potential techniques with applications in the fields of inverse problems, band gap structures, and optimal design, in particular the optimal design of photonic and phononic crystals. Throughout this book, it is shown how powerful the layer potentials techniques are for solving not only boundary value problems but also eigenvalue problems if they are combined with the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. The general approach in this book is developed in detail for eigenvalue problems for the Laplacian and the Lamé system in the following two situations: one under variation of domains or boundary conditions and the other due to the presence of inclusions.

The book will be of interest to researchers and graduate students working in the fields of partial differential equations, integral equations, and inverse problems. Researchers in engineering and physics may also find this book helpful.

Readership

Graduate students and research mathematicians interested in PDE's, integral equations, and spectral analysis.

  • Chapters
  • Introduction
  • Gohberg-Sigal theory
  • 1. Generalized argument principle and Rouché’s theorem
  • Eigenvalue perturbation problems and applications
  • 2. Layer potentials
  • 3. Eigenvalue perturbations of the Laplacian
  • 4. Vibration testing for detecting internal corrosion
  • 5. Perturbations of scattering frequencies of resonators with narrow slits and slots
  • 6. Eigenvalue perturbations of the Lamé system
  • Photonic and phononic band gaps and optimal design
  • 7. Floquet transform, spectra of periodic elliptic operators, and quasi-periodic layer potentials
  • 8. Photonic band gaps
  • 9. Phononic band gaps
  • 10. Optimal design problems
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