Geodesic
The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral
Matematičeskie zametki, Tome 70 (2001) no. 3, pp. 403-418

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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 $a$, we prove uniqueness theorems or present exact formulas for the dimension of the solution space of the Dirichlet problem. 
@article{MZM_2001_70_3_a7,
     author = {H. Matevossian},
     title = {The {Exterior} {Dirichlet} {Problem} for the {Biharmonic} {Equation:} {Solutions} with {Bounded} {Dirichlet} {Integral}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {403--418},
     publisher = {mathdoc},
     volume = {70},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a7/}
}
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H. Matevossian. The Exterior Dirichlet Problem for the Biharmonic Equation: Solutions with Bounded Dirichlet Integral. Matematičeskie zametki, Tome 70 (2001) no. 3, pp. 403-418. http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a7/