A choice of an optimal form of surface cracks in 3D solids

We consider 3D-elastic body with a surface crack satisfying a nonpenetration conditions (Signorini-type conditions). In the paper, we investigate two optimization problems. The first problem is to find the crack shape which gives the minimum deviation of the energy functional derivative from a given critical value. The second one is to investigate a solvability of an optimization problem of a crack path with a cost functional depending on the derivative of the energy functional and a crack surface area.