Layer Potential Techniques in Spectral Analysis (Mathematical Surveys and Monographs)

Habib Ammari, Hyeonbae Kang, and Hyundae Lee

ISBN 10: 0821847848 / ISBN 13: 9780821847848

Published by American Mathematical Society, 2009

About this Item

Offers 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. This book is suitable for researchers and graduate students. Series: Mathematical Surveys and Monographs. Num Pages: 202 pages, Illustrations. BIC Classification: PBKJ; PBW. Category: (UP) Postgraduate, Research & Scholarly. . . 2009. Hardcover. . . . .

Seller Inventory # V9780821847848

Bibliographic Details

• Title: Layer Potential Techniques in Spectral Analysis (Mathematical Surveys and Monographs)
• Publisher: American Mathematical Society
• Publication Date: 2009
• Language: English
• ISBN 10: 0821847848
• ISBN 13: 9780821847848
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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 Lame 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.