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

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
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