K. Eppler : Optimal shape design for elliptic equations via BIE-methods

Author(s) :

K. Eppler

Title :

Optimal shape design for elliptic equations via BIE-methods

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-10, 1998

Mathematics Subject Classification :

49Q10 [ Optimization of the shape other than minimal surfaces ]

49K20 [ Optimal control problems with PDE (nec./ suff.) ]

31A10 [ Integral representations of harmonic functions (two-dimensional) ]

Abstract :

For shape optimization problem a special approach for the description of the boundary variation is investigated. This, together with the use of a potential ansatz for the state, allows a natural embedding of the problem in a Banach space. Therefore, the standard differential calculus can be applied in order to prove Frechet-differentiability of the objective for appropriately choosen data (sufficiently smooth). Moreover, necessary optimality conditions are obtained, which can be expressed in terms of an adjoint state for more regular data.

Keywords :

optimal shape design, fundamental solution, boundary integral equation, first-order necessary conditions

Language :

english

Publication time :

5/1998