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Mathematical Surveys and Monographs
2009; 202 pp; hardcover
List Price: US$73
Member Price: US$58.40
Order Code: SURV/153
Inverse Problems, Multi-Scale Analysis, and Effective Medium Theory - Habib Ammari and Hyeonbae Kang
Tools for PDE: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials - Michael E Taylor
Morse Theoretic Aspects of \(p\)-Laplacian Type Operators - Kanishka Perera, Ravi P Agarwal and Donal O'Regan
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.
Graduate students and research mathematicians interested in PDE's, integral equations, and spectral analysis.
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