K.Eppler : On the symmetry od second derivatives in optimal shape design and sufficient optimality conditions for shape functionals

Author(s) :

K.Eppler

Title :

On the symmetry od second derivatives in optimal shape design and sufficient optimality conditions for shape functionals

Electronic source:

application/pdf

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-11, 1998

Mathematics Subject Classification :

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

58C20 [ Generalized differentiation theory on manifolds ]

49K10 [ Free problems in several independent variables (nec./ suff.) ]

Abstract :

For some heuristic approaches of the variation in shape optimization the computation of second derivatives of domain and boundary integral functionals, their symmetry and a comparison to the velocity field or material derivative method are discussed. Moreover, for some of these approaches the functionals are Frechet-differentiable, because an embedding into a Banach space problem is possible. This allows the discussion of sufficient condition in terms of a coercivity assumption on the second Frechet-derivative. The theory is illustrated by a discussion of the famous Dido problem.

Keywords :

optional shape design, second directional derivatives, boundary integral eqation

Language :

english

Publication time :

10/1998