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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