Ebook: Variational Methods in Shape Optimization Problems

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.

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The study of shape optimization problems involves a wide area of academic research and applications to the real world. In this work these problems are treated from 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:* Presents foundational introduction to shape optimization theory* Studies some classical problems: the isoperimetric problem and the Newton problem involving the best aerodynamical shape, optimization problems over classes of convex domains* Treats optimal control problems under a general scheme, giving a topological framework, a survey of G-convergence, problems governed by ODE* Examines shape optimization problems with Dirichlet and Neumann condition on the free boundary, the existence of classical solutions* Poses some open questionsDriven by several good examples and illustrations, the book requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis.