Extremum Problems for Eigenvalues of Elliptic Operators / by Antoine Henrot
(Frontiers in Mathematics)
| データ種別 | 電子ブック |
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| 出版者 | Basel : Birkhäuser Basel |
| 出版年 | 2006 |
| 本文言語 | 英語 |
| 大きさ | X, 202 p. 16 illus : online resource |
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| 内容注記 | Eigenvalues of elliptic operators Tools The first eigenvalue of the Laplacian-Dirichlet The second eigenvalue of the Laplacian-Dirichlet The other Dirichlet eigenvalues Functions of Dirichlet eigenvalues Other boundary conditions for the Laplacian Eigenvalues of Schrödinger operators Non-homogeneous strings and membranes Optimal conductivity The bi-Laplacian operator |
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| 一般注記 | 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 |
| 著者標目 | *Henrot, Antoine author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Operator theory LCSH:Potential theory (Mathematics) FREE:Mathematics FREE:Operator Theory FREE:Potential Theory |
| 分 類 | DC23:515.724 |
| 巻冊次 | ISBN:9783764377069 
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| ISBN | 9783764377069 |
| URL | http://dx.doi.org/10.1007/3-7643-7706-2 |
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