1 option
Shape optimization : variations of domains and applications / Catherine Bandle, Alfred Wagner.
- Format:
- Book
- Author/Creator:
- Bandle, Catherine, author.
- Wagner, Alfred, author.
- Series:
- De Gruyter series in nonlinear analysis and applications ; v. 42.
- De Gruyter series in nonlinear analysis and applications ; Volume 42
- Language:
- English
- Subjects (All):
- Shape theory (Topology).
- Calculus of variations.
- Nonlinear functional analysis.
- Physical Description:
- 1 online resource (xi, 278 pages) : illustrations
- Edition:
- 1st ed.
- Place of Publication:
- Berlin ; Boston : De Gruyter, [2023].
- Summary:
- "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."--Provided by publisher.
- Contents:
- Intro
- 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 &
- lt
- 0
- 12 Problems with infinitely many positive and negative eigenvalues
- 13 The torsion problem for α &
- 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.
- Notes:
- Includes bibliographical references (pages 271-275) and index.
- Description based on online resource (viewed Dec 4, 2023) publisher supplied metadata and other sources.
- Description based on publisher supplied metadata and other sources.
- Other Format:
- Print version : Catherine Bandle Shape optimization
- ISBN:
- 9783111025810
- 9783111025438
- 3111025438
- OCLC:
- 1382425152
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.