Variational Methods in Shape Optimization Problems

Shape optimization problems are treated from the classical and modern perspectives§Targets 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§Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis§Driven by several good examples and illustrations§Poses some open questions.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.