Optimal shape design for elliptic equations via BIE-methods - Eppler, Karsten (Zielona Góra: Uniwersytet Zielonogórski)
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