
Introduction  Preview Material  Table of Contents  Supplementary Material 
Mathematical Surveys and Monographs 2009; 202 pp; hardcover Volume: 153 ISBN10: 0821847848 ISBN13: 9780821847848 List Price: US$73 Member Price: US$58.40 Order Code: SURV/153 See also: Inverse Problems, MultiScale 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 doublelayer potentials to treat classical boundary value problems. The aim of this book is to give a selfcontained 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 operatorvalued 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. 


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