TU Chemnitz, Fakultät für Mathematik: Fakultät für Mathematik
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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) ]
- 49K20 [ Optimal control problems with PDE (nec./ suff.) ]
- 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
