Geodesic
Solutions of exterior boundary-value problems for the elasticity system in weighted spaces
Sbornik. Mathematics, Tome 192 (2001) no. 12, pp. 1763-1798 Cet article a éte moissonné depuis la source Math-Net.Ru

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The properties of generalized solutions of the exterior Dirichlet and Neumann boundary-value problems are studied for the stationary linear system of elasticity theory in unbounded domains under the assumption that generalized solutions of these problems have finite energy integrals with weight $|x|^a$. Depending on the value of the parameter $a$ uniqueness results are established and explicit formulae for the dimension of the space of solutions of the exterior boundary-value problems are obtained. 
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H. Matevossian. Solutions of exterior boundary-value problems for the elasticity system in weighted spaces. Sbornik. Mathematics, Tome 192 (2001) no. 12, pp. 1763-1798. http://geodesic.mathdoc.fr/item/SM_2001_192_12_a1/

[1] Fredholm J., “Solution d'un problème fondamental de la théorie d'élasticité”, Ark. Math. Astronom. Fys., 2:28 (1906), 3–8

[2] Korn A., “Solution générale du problème d'équilibre dans la théorie d'élasticité dans le cas où les efforts sont données à la surface”, Ann. Fac. Sci. Univ. Toulouse, 10 (1908), 165–269 | MR | Zbl

[3] Friedrichs K. O., “On the boundary of value problems of the theory of elasticity and Korn's inequality”, Ann. of Math. (2), 48:2 (1947), 441–471 | DOI | MR | Zbl

[4] Fikera G., Teoremy suschestvovaniya v teorii uprugosti, Mir, M., 1974

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

[6] Kondratev V. A., Oleinik O. A., “O neravenstvakh Korna i edinstvennosti reshenii klassicheskikh kraevykh zadach v neogranichennykh oblastyakh dlya sistemy teorii uprugosti”, Sovremennye problemy matematicheskoi fiziki, T. 1, Izd-vo Tbil. un-ta, Tbilisi, 1987, 35–63 | MR

[7] Kondratiev V. A., Oleinik O. A., “Hardy's and Korn's type inequalities and their applications”, Rend. Mat. Appl. (7), 10 (1990), 641–666 | MR | Zbl

[8] Kondratiev V. A., Oleinik O. A., “Sur un problème de E. Sanchez-Palencia”, C. R. Acad. Sci. Paris Sér. I Math., 299:15 (1984), 745–748 | MR | Zbl

[9] Kondratev V. A., Oleinik O. A., “O periodicheskikh po vremeni resheniyakh parabolicheskogo uravneniya vtorogo poryadka vo vneshnikh oblastyakh”, Vestn. MGU. Ser. 1. Matem., mekh., 1985, no. 4, 38–47 | MR | Zbl

[10] 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

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

[12] 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

[13] Buchukuri T. V., Gegeliya T. G., “O edinstvennosti reshenii osnovnykh zadach teorii uprugosti dlya beskonechnykh oblastei”, Differents. uravneniya, 25:9 (1989), 1556–1565 | MR | Zbl

[14] Lopatinskii Ya. B., Teoriya obschikh granichnykh zadach. Izbrannye trudy, Naukova dumka, Kiev, 1984 | MR

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

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

[17] Oleinik O. A., Iosifyan G. A., Shamaev A. S., Matematicheskie zadachi teorii silno neodnorodnykh uprugikh sred, Izd-vo MGU, M., 1990 | Zbl

[18] Mosolov P. P., Myasnikov I. P., “Dokazatelstvo neravenstva Korna”, Dokl. AN SSSR, 201:1 (1971), 36–39 | MR | Zbl

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

[20] Bers L., Dzhon F., Shekhter M., Uravneniya s chastnymi proizvodnymi, Mir, M., 1966 | MR | Zbl