Shape sensitivity analysis of problems with singularities. (English) Zbl 0984.49024

Fremiot, Gilles; Sokolowski, Jan

Cagnol, John et al., Shape optimization and optimal design. Proceedings of the IFIP conference. Selected papers from the sessions ”Distributed parameter systems” and ”Optimization methods and engineering design” held within the 19th conference system modeling and optimization, Cambridge, GB, July 12-16, 1999. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 216, 255-276 (2001).

The authors prove a representation theorem for the shape derivative of functionals depending on solutions of boundary value problems defined in sets with geometric singularities. The result is applied to a control problem with the state equation in the form of the Dirichlet-Neumann boundary value problem. Moreover, the shape derivative of the first eigenvalue of the Laplacian in a domain with a crack is evaluated.
For the entire collection see [Zbl 0959.00036].

Reviewer: Dian K.Palagachev (Bari)

MSC:

49Q12	Sensitivity analysis for optimization problems on manifolds
49Q10	Optimization of shapes other than minimal surfaces

Keywords:

problems with singularities; shape sensitivity analysis