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Paper details
Number 3 - September 2000
Volume 10 - 2000
Optimal shape design for elliptic equations via BIE-methods
Karsten Eppler
Abstract
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 Frechét-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.
Keywords
optimal shape design, fundamental solution, boundary integral equation, first-order necessary condition