Extremum Problems for Eigenvalues of Elliptic Operators

• Main Author: Henrot, Antoine (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2006.
• Series: Frontiers in Mathematics,
• Subjects: Mathematics.; Operator theory.; Potential theory (Mathematics).; Operator Theory.; Potential Theory.

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 eigenval...

Table of Contents:

• 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.