Mixed Dirichlet–Steklov problem for the biharmonic equation in weighted spaces
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 31 (2016) no. 31, pp. 87-109 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We address the uniqueness of weak solutions of the mixed Dirichlet–Steklov problem for the biharmonic equation in the exterior of a compact set in the class of functions having a finite Dirichlet integral with the weight $|x|^a$. Depending on the parameter $a$, we establish some uniqueness theorems and obtain precise formulas for the dimension of the space of solutions.
@article{TSP_2016_31_31_a4,
     author = {H. A. Matevossian},
     title = {Mixed {Dirichlet{\textendash}Steklov} problem for the biharmonic equation in weighted spaces},
     journal = {Trudy Seminara im. I.G. Petrovskogo},
     pages = {87--109},
     year = {2016},
     volume = {31},
     number = {31},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a4/}
}
TY  - JOUR
AU  - H. A. Matevossian
TI  - Mixed Dirichlet–Steklov problem for the biharmonic equation in weighted spaces
JO  - Trudy Seminara im. I.G. Petrovskogo
PY  - 2016
SP  - 87
EP  - 109
VL  - 31
IS  - 31
UR  - http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a4/
LA  - ru
ID  - TSP_2016_31_31_a4
ER  - 
%0 Journal Article
%A H. A. Matevossian
%T Mixed Dirichlet–Steklov problem for the biharmonic equation in weighted spaces
%J Trudy Seminara im. I.G. Petrovskogo
%D 2016
%P 87-109
%V 31
%N 31
%U http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a4/
%G ru
%F TSP_2016_31_31_a4
H. A. Matevossian. Mixed Dirichlet–Steklov problem for the biharmonic equation in weighted spaces. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 31 (2016) no. 31, pp. 87-109. http://geodesic.mathdoc.fr/item/TSP_2016_31_31_a4/

[1] Kudryavtsev L. D., “Reshenie pervoi kraevoi zadachi dlya samosopryazhennykh i ellipticheskikh uravnenii v sluchae neogranichennykh oblastei”, Izv. AN SSSR. Ser. matem., 31:5 (1967), 354–336

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

[3] Kondratiev V. A., Oleinik O. A., “Hardy's and Korn's inequality and their application”, Rend. Mat. Appl. Ser. VII, 10 (1990), 641–666 | MR | Zbl

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

[5] Kondratev V. A., Oleinik O. A., Kopachek I., “Ob asimptoticheskikh svoistvakh reshenii bigarmonicheskogo uravneniya”, Differents. uravneniya, 17:10 (1981), 1886–1899 | MR | Zbl

[6] Kondratiev V. A., Oleinik O. A., “Estimates for solutions of the Dirichlet problem for biharmonic equation in a neighbourhood of an irregular boundary point and in a neighbourhood of infinity Saint-Venant's principle”, Proc. Royal Soc. Edinburgh, 93A (1983), 327–343 | DOI | MR | Zbl

[7] 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

[8] Matevosyan O. A., “O resheniyakh vneshnei zadachi Dirikhle dlya bigarmonicheskogo uravneniya s konechnym vesovym integralom Dirikhle”, Matem. zametki, 70:3 (2001), 403–418 | DOI | MR | Zbl

[9] Matevosyan O. A., “O resheniyakh vneshnikh kraevykh zadach dlya sistemy teorii uprugosti v vesovykh prostranstvakh”, Matem. sb., 192:12 (2001), 25–60 | DOI

[10] Matevosyan O. A., “O resheniyakh smeshannykh kraevykh zadach dlya sistemy teorii uprugosti v neogranichennykh oblastyakh”, Izv. RAN. Ser. matem., 67:5 (2003), 49–82 | DOI | MR | Zbl

[11] Matevosyan O. A., “On solutions of one boundary value problem for the polyharmonic equation in unbounded domains”, Russ. J. Math. Phys., 21:1 (2014), 130–132 | DOI | MR | Zbl

[12] Matevossian H. A., “On solutions of the Dirichlet problem for the polyharmonic equation in unbounded domains”, P-Adic Numbers, Ultrametric Analysis Appl., 7:1 (2015), 74–78 | MR

[13] Matevosyan O. A., “Reshenie smeshannoi kraevoi zadachi dlya bigarmonicheskogo uravneniya s konechnym vesovym integralom Dirikhle”, Differents. uravneniya, 51:4 (2015), 481–494 | DOI | Zbl

[14] Matevossian H. A., “On solutions of the Dirichlet–Steklov problem for the biharmonic equation in exterior domains”, P-Adic Numbers, Ultrametric Anal. Appl., 8:4 (2016), 343–350 | MR

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

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

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

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