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STUDIA MATHEMATICA - Issue no. 3 / 2006 | |||||||
Article: |
BOOK REVIEWS - DORIN BUCUR, GIUSEPPE BUTTAZZO, VARIATIONAL METHODS IN SHAPE OPTIMIZATION PROBLEMS, PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, BIRKH¨AUSER, 2005, ISBN 0-8176-4359-1.. Authors: DANIELA INOAN. |
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Abstract: Usually, problems of the calculus of variations concern optimization among an admissible class of functions. What is special about shape optimization problems is that the ”competing objects” are shapes (domains of Rn). Because of this, the existence of a solution is ensured only in certain cases, due to some geometrical restrictions on the admissible domains (shapes) or to a particular form of the cost function. In general, relaxed formulations of the problems have to be formulated. | |||||||