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Optimal Shape Design is concerned with the optimization of some
performance criterion dependent (besides the constraints of the
problem) on the "shape" of some region. The main topics covered
are: the optimal design of a geometrical object, for instance a
wing, moving in a fluid; the optimal shape of a region (a harbor),
given suitable constraints on the size of the entrance to the
harbor, subject to incoming waves; the optimal design of some
electrical device subject to constraints on the performance. The
aim is to show that Optimal Shape Design, besides its interesting
industrial applications, possesses nontrivial mathematical aspects.
The main theoretical tools developed here are the homogenization
method and domain variations in PDE. The style is mathematically
rigorous, but specifically oriented towards applications, and it is
intended for both pure and applied mathematicians. The reader is
required to know classical PDE theory and basic functional
analysis.
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