Geodesic
Optimal Shape Design for Elliptic Equations Via Bie-Methods
International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 3, pp. 487-516.

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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.
Keywords: optimal shape design, fundamental solution, boundary integral equation, first-order necessary condition
Mots-clés : rozwiązanie podstawowe, równanie całkowe 
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     author = {Eppler, K.},
     title = {Optimal {Shape} {Design} for {Elliptic} {Equations} {Via} {Bie-Methods}},
     journal = {International Journal of Applied Mathematics and Computer Science},
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     number = {3},
     year = {2000},
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     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2000_10_3_a2/}
}
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Eppler, K. Optimal Shape Design for Elliptic Equations Via Bie-Methods. International Journal of Applied Mathematics and Computer Science, Tome 10 (2000) no. 3, pp. 487-516. http://geodesic.mathdoc.fr/item/IJAMCS_2000_10_3_a2/