Shape Optimization : : Variations of Domains and Applications / / Catherine Bandle, Alfred Wagner.
This book investigates how domain dependent quantities from geometry and physics behave when the domain is perturbed. Of particular interest are volume- and perimeter-preserving perturbations. The first and second derivatives with respect to the perturbation are exploited for domain functionals like...
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| Superior document: | Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1 |
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| VerfasserIn: | |
| Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2023] ©2023 |
| Year of Publication: | 2023 |
| Language: | English |
| Series: | De Gruyter Series in Nonlinear Analysis and Applications ,
42 |
| Online Access: | |
| Physical Description: | 1 online resource (XII, 280 p.) |
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Table of Contents:
- Frontmatter
- Preface
- Contents
- 1 Overview of the basic problems
- 2 Basic concepts
- 3 Spherical harmonics and eigenvalue problems
- 4 Variational formulas
- 5 Geometric inequalities, convolutions, cost functions
- 6 Domain variations for energies
- 7 Discussion of the main results
- 8 General strategy and applications
- 9 Eigenvalue problems
- 10 Quantitative estimates
- 11 The Robin eigenvalues for α < 0
- 12 Problems with infinitely many positive and negative eigenvalues
- 13 The torsion problem for α < 0
- 14 Problems in annular domains
- 15 The first buckling eigenvalue of a clamped plate
- 16 A fourth order Steklov problem
- A General remarks
- B Geometry
- C Sobolev spaces and inequalities
- D Bilinear forms
- Notation
- Bibliography
- Index