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＜電子ブック＞
Variational Methods in Shape Optimization Problems / by Dorin Bucur, Giuseppe Buttazzo
(Progress in Nonlinear Differential Equations and Their Applications. ISSN:23740280 ; 65)

版	1st ed. 2005.
出版者	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
出版年	2005
本文言語	英語
大きさ	VIII, 216 p : online resource
著者標目	*Bucur, Dorin author Buttazzo, Giuseppe author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Differential equations LCSH:Functional analysis LCSH:Difference equations LCSH:Functional equations LCSH:Mathematics FREE:Calculus of Variations and Optimization FREE:Optimization FREE:Differential Equations FREE:Functional Analysis FREE:Difference and Functional Equations FREE:Applications of Mathematics
一般注記	to Shape Optimization Theory and Some Classical Problems -- Optimization Problems over Classes of Convex Domains -- Optimal Control Problems: A General Scheme -- Shape Optimization Problems with Dirichlet Condition on the Free Boundary -- Existence of Classical Solutions -- Optimization Problems for Functions of Eigenvalues -- Shape Optimization Problems with Neumann Condition on the Free Boundary The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems. Key topics and features: * Presents foundational introduction to shape optimization theory * Studies certain classical problems: the isoperimetric problem and the Newton problem involving the best aerodynamical shape, and optimization problems over classes of convex domains * Treats optimal control problems under a general scheme, giving a topological framework, a survey of "gamma"-convergence, and problems governed by ODE * Examines shape optimization problems with Dirichlet and Neumann conditions on the free boundary, along with the existence of classical solutions * Studies optimization problems for obstacles and eigenvalues of elliptic operators * Poses several open problems for further research * Substantial bibliography and index Driven by good examples and illustrations and requiring only a standard knowledge in the calculus of variations, differential equations, and functional analysis, the book can serve as a text for a graduate course in computational methods of optimal design and optimization, as well as an excellent reference for applied mathematicians addressing functional shape optimization problems HTTP:URL=https://doi.org/10.1007/b137163

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