Solution of a mixed boundary value problem for the biharmonic equation with finite weighted Dirichlet integral

We study the uniqueness of the solution of a mixed boundary value problem for the biharmonic equation in the exterior of a compact set under the assumption that the generalized solution of that problem has a finite Dirichlet integral with weight |x| a . Depending on the value of the parameter a, we prove uniqueness theorems and obtain exact formulas for the dimension of the solution space of the mixed boundary value problem.