ENGLISH

Extremum Problems for Eigenvalues of Elliptic Operators (Frontiers in Mathematics)

By Antoine Henrot

Book information

Year
2006
ISBN
3764377054, 9783764377069, 9783764377052
LCC
QA193 .H46 2006
Open Library ID
OL19811839M
Language
english
Format
PDF
Filesize
1 MB (1442530 bytes)
Edition
1
Pages
205\205
Orientation
yes
Scanned
no
Time added
2011-06-04 13:46:07

Description

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.

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