Extremum Problems for Eigenvalues of Elliptic Operators
By addebook • Jun 28th, 2008 • Category: Mathematics
Extremum Problems for Eigenvalues of Elliptic Operators (Frontiers in Mathematics)
By Antoine Henrot
Publisher: Birkhäuser Basel
Number Of Pages: 202
Publication Date: 2006-08-29
Sales Rank: 2054604
ISBN / ASIN: 3764377054
EAN: 9783764377052
Binding: Paperback
Manufacturer: Birkhäuser Basel
Studio: Birkhäuser Basel
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 Schrodinger 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.
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