Fréchet-Differentiability and Sufficient Optimality Conditions for Shape Functionals
Karsten Eppler · Birkhäuser Basel eBooks · 1999
For a heuristic approach of the boundary variation in shape optimization, applicable for a special class of domains, the computation of second derivatives of domain and boundary integral functional are discussed. Moreover, for this approach the functional are Préchet-differentiable, because an embedding into a Banach space problem is possible. This implies symmetry and allows the discussion of sufficient condition in terms of a coercivity assumption on the second Fréchet-derivative. The theory is illustrated by a discussion of the Dido problem.