Geodesic
Boundary value problems for generalized differential equations
Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 267-287 
V. A. Bulychev; F. F. Frolov. Boundary value problems for generalized differential equations. Sbornik. Mathematics, Tome 63 (1989) no. 2, pp. 267-287. http://geodesic.mathdoc.fr/item/SM_1989_63_2_a0/
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     author = {V. A. Bulychev and F. F. Frolov},
     title = {Boundary value problems for generalized differential equations},
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     volume = {63},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_63_2_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new approach to boundary value problems for generalized differential equations is considered. It is shown how to obtain the formulations of boundary value problems studied earlier in the framework of this approach. Properties involving the solvability of such problems are expressed in terms of certain boundary spaces consisting of generalized functions with supports on the boundary. Possible methods for solving boundary value problems arising in this scheme are discussed. The Markov property is obtained for a solution of a boundary value problem for a generalized stochastic differential equation with Markov source. Bibliography: 11 titles.

[1] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Izd-vo LGU, L., 1950

[2] Vishik M. I., “Ob obschem vide razreshimykh kraevykh zadach dlya odnorodnogo i neodnorodnogo ellipticheskogo differentsialnogo uravneniya”, DAN SSSR, 82:2 (1952), 181–184 | Zbl

[3] Vishik M. I., “Ob obschikh kraevykh zadachakh dlya ellipticheskikh differentsialnykh uravnenii”, Tr MMO, 1 (1952), 187–246

[4] Rozanov Yu. A., “Obobschennaya zadacha Dirikhle”, DAN SSSR, 266:5 (1982), 1067–1069 | MR | Zbl

[5] Rozanov Yu. A., “O nekotorykh obobscheniyakh zadachi Dirikhle”, Matem. sb., 120(162) (1983), 291–310 | MR

[6] Rozanov Yu. A., “O printsipe Markova–Kolmogorova dlya stokhasticheskikh differentsialnykh uravnenii”, Teoriya veroyatnostei i ee primeneniya, 28:2 (1983), 362–366 | MR

[7] Rozanov Yu. A., “Obschie granichnye zadachi dlya lineinykh differentsialnykh operatorov i metod sopryazhennykh uravnenii”, Tr. MIAN, 166 (1984), 213–221 | MR | Zbl

[8] Rozanou Yu. A., Boundary problems for stochastic partial differential equations, Preprint Res. Cent. Bielefeld–Bochum–Stochastics Univ. of Bielefeld, No 23, Bielefeld, 1985

[9] Rozanov Yu. A., Markovskie sluchainye polya, Nauka, M., 1981 | MR | Zbl

[10] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983 | MR

[11] Bulychëv V. A., “Markovskoe svoistvo evolyutsionnogo stokhasticheskogo uravneniya”, Teoriya veroyatnostei i ee primeneniya, 31:2 (1986), 373—378 | MR