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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.

Computer. Automation --- automatisering --- toegepaste wiskunde --- Functional analysis --- Mathematics --- differentiaalvergelijkingen --- kansrekening --- wiskunde --- Operational research. Game theory --- Partial differential equations --- functies (wiskunde) --- Mathematical optimization --- Shapes --- Optimisation mathématique --- Formes --- EPUB-LIV-FT SPRINGER-B LIVMATHE --- Mathematical optimization. --- Shapes. --- Differential equations, partial. --- Functional analysis. --- Functional equations. --- Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization. --- Partial Differential Equations. --- Functional Analysis. --- Difference and Functional Equations. --- Applications of Mathematics. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Math --- Science --- Equations, Functional --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Calculus of variations. --- Partial differential equations. --- Difference equations. --- Applied mathematics. --- Engineering mathematics. --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Isoperimetrical problems --- Variations, Calculus of --- Engineering --- Engineering analysis --- Differential equations, Partial.

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"Shape optimization and spectral theory" is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization.It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results.Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributorsAntunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noël Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartłomiej A., Velichkov Bozhidar

MATHEMATICS / Optimization.