On the statements and solvability of the problems on the contact of two plates containing rigid inclusions

We consider problems with an unknown boundary about the contact of two elastic plates situated at an angle to each other. Each of the plates contains a rigid inclusion. The lower plate is deformed in its plane, and the upper plate, in the vertical direction. We establish the solvability and the uniqueness of the solutions to the problems. Assuming sufficient smoothness of the solution for various cases of the location of the rigid inclusions, we obtain a differential statement of the problem equivalent to the variational statement. The equilibrium equations of plates are fulfilled in nonsmooth domains, and the boundary conditions have the form of equalities and inequalities. We consider the limit case corresponding to the increase of the rigidity parameter of the lower plate to infinity.