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Shape Optimization
Variations of Domains and Applications
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Catherine Bandle
Language:
English
Published/Copyright:
2023
About this book
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 eigenvalues, energies and geometrical quantities. They provide necessary conditions for optimal domains and are useful when global approaches like symmetrizations fail. The book is exampledriven and illustrates the usefulness of domain variations in various applications.
- Comprehensive derivation of the variation formulas applying to functionals from geometry and physics.
- Presents the main tools from calculus and geometry to calculate formulas.
- Develops strategies for determination of local maxima and minima
Author / Editor information
Catherine Bandle, Universität Basel, Switzerland; Alfred Wagner, RWTH Aachen University, Germany.
Topics
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Frontmatter
I -
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Preface
V -
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Contents
VII -
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1 Overview of the basic problems
1 -
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2 Basic concepts
7 -
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3 Spherical harmonics and eigenvalue problems
38 -
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4 Variational formulas
52 -
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5 Geometric inequalities, convolutions, cost functions
71 -
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6 Domain variations for energies
99 -
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7 Discussion of the main results
119 -
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8 General strategy and applications
131 -
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9 Eigenvalue problems
148 -
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10 Quantitative estimates
167 -
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11 The Robin eigenvalues for α < 0
173 -
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12 Problems with infinitely many positive and negative eigenvalues
188 -
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13 The torsion problem for α < 0
195 -
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14 Problems in annular domains
206 -
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15 The first buckling eigenvalue of a clamped plate
217 -
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16 A fourth order Steklov problem
236 -
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A General remarks
253 -
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B Geometry
257 -
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C Sobolev spaces and inequalities
263 -
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D Bilinear forms
265 -
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Notation
269 -
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Bibliography
271 -
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Index
277
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 19, 2023
eBook ISBN:
9783111025438
Hardcover published on:
June 19, 2023
Hardcover ISBN:
9783111025261
Pages and Images/Illustrations in book
Front matter:
12
Main content:
280
Illustrations:
27
Keywords for this book
Shape Optimization; Domain Variation; Pertubation; Spherical Harmonics; Eigenvalues
Audience(s) for this book
Institutional Libraries, graduate students and researchers with a background in classical analysis.
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
