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. 
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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/

[1] Kudryavtsev L. D., “Reshenie pervoi kraevoi zadachi dlya samosopryazhennykh ellipticheskikh uravnenii v sluchae neogranichennoi oblasti”, Izv. AN SSSR. Ser. matem., 31:5 (1967), 1179–1199 | MR | Zbl

[2] Kondratev V. A., Oleinik O. A., “Teoremy edinstvennosti resheniya vneshnikh kraevykh zadach i analog printsipa Sen-Venana”, UMN, 39:4 (1984), 165–166 | MR | Zbl

[3] Kondratev V. A., Oleinik O. A., “Kraevye zadachi dlya sistemy teorii uprugosti v neogranichennykh oblastyakh. Neravenstva Korna”, UMN, 43:5 (1988), 55–98 | MR

[4] Konkov A. A., “O razmernosti prostranstva reshenii ellipticheskikh sistem v neogranichennykh oblastyakh”, Matem. sb., 184:12 (1993), 23–52 | Zbl

[5] Matevosyan O. A., “O edinstvennosti resheniya pervoi kraevoi zadachi teorii uprugosti dlya neogranichennykh oblastei”, UMN, 48:6 (1993), 159–160 | MR | Zbl

[6] Matevosyan O. A., “O resheniyakh kraevykh zadach dlya sistemy teorii uprugosti i bigarmonicheskogo uravneniya v poluprostranstve”, Differents. uravneniya, 34:6 (1998), 806–811 | MR | Zbl

[7] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konechnymi ili uglovymi tochkami”, Tr. MMO, 16, URSS, M., 1967, 209–292 | MR | Zbl

[8] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988

[9] Kondratiev V. A., Oleinik O. A., “On the behaviour at infinity of solutions of elliptic systems with a finite energy integral”, Arch. Rat. Mech. Anal., 99:1 (1987), 75–99 | DOI | MR | Zbl

[10] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | Zbl

[11] Mikhlin S. G., Lineinye uravneniya v chastnykh proizvodnykh, Vysshaya shkola, M., 1977