Optimal control of the rigidity of an inclusion in an elastic body

A three-dimensional elastic body with an inclusion is considered. There is a crack part of which is situated on the boundary of the inclusion. On the crack edges, there are given boundary conditions of the type of equalities and inequalities. We consider optimal control problem that allows to choose the safest inclusion from the standpoint of Griffith's criterion. An existence theorem of a solution to the optimal control problem is proved.