Abstract:
In this paper we consider an analog of the obstacle problem for a mechanical system composed of strings and membranes; as well as a generalization of this problem to multidimensional case. Small displacements of this system under external small loads may be modeled as an elliptic equation of second order (outside of a contact zone) on the stratified set, equipped with Dirichlet's condition on the boundary. The main result of this job is a proof of solvability of a corresponding boundary value problem in sobolev-type space. The main assumption is so-called firmness of the stratified set.
