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Optimal Shape Design for Elliptic Equations Via Bie-Methods

Eppler K.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 3

487-516

A special description of the boundary variation in a shape optimization problem is investigated. This, together with the use of a potential theory for the state, result in natural embedding of the problem in a Banach space. Therefore, standard differential calculus can be applied in order to prove the Frechet-differentiability of the cost function for appropriately chosen data (sufficiently smooth). Moreover, necessary optimality conditions are obtained in a similar way as in other approaches, and are expressed in terms of an adjoint state for more regular data.