Second order sensitivity analysis for a class of shape optimization problems-towards a CAD system

Deals with a class of shape optimization problems with a boundary integral as an objective functional. These shape optimization problems arise in various industrial applications such as minimum drag designs in fluid mechanics, designs of plasma shapes in tokamak devices. Deriving second order variations of the objective functionals, the author gives a set of the second order necessary conditions of Kuhn-Tucker-Fujii type. To this end, the author used also the second order variation of a solution of a boundary value problem that is a constraint to the optimization problems. As a byproduct of these analyses, the author obtains a numerical method for the solutions of the optimization problems