Overview
- Self-contained presentation of classical isoperimetric inequalities for eigenvalues
- Collection of almost all questions related to extremum problems for eigenvalues
- Includes supplementary material: sn.pub/extras
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Problems linking the shape of a domain or the coefficients of an elliptic operator to the sequence of its eigenvalues are among the most fascinating of mathematical analysis. In this book, we focus on extremal problems. For instance, we look for a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. We also consider the case of functions of eigenvalues. We investigate similar questions for other elliptic operators, such as the Schrödinger operator, non homogeneous membranes, or the bi-Laplacian, and we look at optimal composites and optimal insulation problems in terms of eigenvalues.
Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory.
Reviews
From the reviews:
"The book is a good collection of extremal problems for eigenvalues of elliptic operators and it gives a good account of the present state of research. It presents 30 open problems and is an absolutely necessary starting point for research work in this field. All proofs are strictly rigorous and the author refers for some other proofs to the bibliography, which contains 215 references. The material is interesting for specialists in both pure and applied mathematics, and can also be used in students' work." —Mathematical Reviews
“This is the first book devoted mainly to this subject and is therefore highly welcome. The book contains many interesting results, documents some recent progress and presents 30 open problems. … The book will help the readers (pure and applied mathematicians interested in this area) to update their knowledge in this lively field of research.” (M. Hoffmann-Ostenhof, Monatshefte für Mathematik, Vol. 159 (3), February, 2010)
Authors and Affiliations
Bibliographic Information
Book Title: Extremum Problems for Eigenvalues of Elliptic Operators
Authors: Antoine Henrot
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/3-7643-7706-2
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2006
Softcover ISBN: 978-3-7643-7705-2Published: 18 July 2006
eBook ISBN: 978-3-7643-7706-9Published: 29 August 2006
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: X, 202
Topics: Operator Theory, Potential Theory