Optimal Design and Relaxation of Variational Problems. II,
MASSACHUSETTS INST OF TECH CAMBRIDGE
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Our optimal design problem as a geometrical solution if and only if a minimizing u exists for the original variational problem. In general this will not be so relaxation yields instead a minimizing sequence and associated designs with increasingly many holes. In the limit, they determine a generalized solution of the design problem, an optimal structure made of composite materials obtained by perforation. The mathematical theory of composite materials is homogenization. It offers another route to understanding optimal design by constructing composite materials with extremal properties.
- Theoretical Mathematics