Abstract:

The form of directional derivative of the metric projection in the Sobolev space $H^2_0(\Omega)$ onto the convex set $K=\{f\in H^2_0(Ø) \vert f\ge\psi\}$ is derived in [14]. In the present paper the result is used to obtain the first order optimality conditions for a class of nonsmooth optimal design problems for the Kirchhoff plate with an obstacle.