Directional differentiability of metric projection in [..] and applications
Résumé
The form of directional derivative of the metric projection in the Sobolev space HS(2;0)() into the convex set K = {f HS(2;0)() | f y } is derived. The result is used to obtain the differential stability of the solutions to obstacle problems for the Kirchhoff plate. Applications to the shape design sensitivity of the obstacle problems are provided.