Extremum Problems for Eigenvalues of Elliptic Operators
By: Henrot, Antoine [author.].
Material type:
BookSeries: Frontiers in Mathematics.Publisher: Basel : Birkh�user Basel, 2006. Description: X, 202 p. 16 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783764377069.DDC classification: 515.724 | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
| PK Kelkar Library, IIT Kanpur | Available | EBKS0007980 |
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 Schr�dinger operators -- Non-homogeneous strings and membranes -- Optimal conductivity -- The bi-Laplacian operator.
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 Schr�dinger 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. 0
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