The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral

We study the unique solvability of the Dirichlet problem for the biharmonic equation in the exterior of a compact set under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight |x|^a. Depending on the value of the parameter ^a,a we prove uniqueness theorems or present exact formulas for the dimension of the solution space of the Dirichlet problem.