On contact of thin obstacle and plate, containing thin inclusion

In this paper, we consider problems describing a contact between an elastic plate and a thin elastic obstacle. The plate has a thin elastic inclusion. Under study is equilibrium problems for the plate both with the presence or absence of a cut. Different equivalent formulations of these problems are proposed, and existence of solutions is proved. We investigate a convergence to infinity of a rigidity parameter of the elastic inclusion. Formulations of the limit problem are analyzed.