Boundary equations in dynamic problems for thin elastic plates with mixed boundary conditions

The dynamic problems for thin elastic plates in the Kirchhoff model with mixed boundary conditions are under consideration. The solutions for the problems are introduced by dynamic analogs of the single and double layers potentials. These representations lead to the pair boundary equations systems with respect to the unknown densities. The main result of work is the prove of solvability of these systems in an one-parameter scale of Sobolev-type function spaces.