On solutions of mixed boundary-value problems for the elasticity system in unbounded domains

We study the properties of generalized solutions of mixed boundary-value problems for the linear system of elasticity theory in the exterior of a compact set and in a half-space under the assumption that the energy integral with weight $|x|^a$ is finite for such solutions. Depending on the value of the parameter $a$, a uniqueness criterion is established for these solutions, and exact formulae are obtained for the dimension of the space of solutions.