Geodesic
On the construction of the Riemann function for the Bianchi equation in an $n$-dimensional spac
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2008), pp. 40-46.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we obtain a more general form of conditions which enable one to construct explicitly the Riemann function for the Bianchi equation.
Mots-clés : Bianchi equation
Keywords: Riemann function. 
@article{IVM_2008_9_a4,
     author = {O. A. Koshcheeva},
     title = {On the construction of the {Riemann} function for the {Bianchi} equation in an $n$-dimensional spac},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {40--46},
     publisher = {mathdoc},
     number = {9},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_9_a4/}
}
TY  - JOUR
AU  - O. A. Koshcheeva
TI  - On the construction of the Riemann function for the Bianchi equation in an $n$-dimensional spac
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 40
EP  - 46
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_9_a4/
LA  - ru
ID  - IVM_2008_9_a4
ER  - 
%0 Journal Article
%A O. A. Koshcheeva
%T On the construction of the Riemann function for the Bianchi equation in an $n$-dimensional spac
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 40-46
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2008_9_a4/
%G ru
%F IVM_2008_9_a4
O. A. Koshcheeva. On the construction of the Riemann function for the Bianchi equation in an $n$-dimensional spac. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2008), pp. 40-46. http://geodesic.mathdoc.fr/item/IVM_2008_9_a4/

[1] Bianchi L., “Sulla estensione del metodo di Riemann alle equiazioni lineari alle derivate parziali d'ordine superiore”, Atti R. Accad. Lincei. Rend. Cl. Sc. fis., mat. e natur., 1 sem., IV, 1895, 133–142

[2] Bateman H., “Logarithmic solutions of Bianchi's equation”, Proc. USA Acad., 19 (1933), 852–854 | DOI | MR

[3] Fage M. K., “Zadacha Koshi dlya uravneniya Bianki”, Matem. sb., 45:3 (1958), 281–322 | MR | Zbl

[4] Bondarenko B. A., Bazisnye sistemy polinomialnykh i kvazipolinomialnykh reshenii uravnenii v chastnykh proizvodnykh, Fan, Tashkent, 1987, 146 pp. | MR

[5] Fage M. K., Nagnibida N. I., Problema ekvivalentnosti obyknovennykh lineinykh differentsialnykh operatorov, Nauka, Novosibirsk, 1987, 280 pp. | MR | Zbl

[6] Zhegalov V. I., Mironov A. N., Differentsialnye uravneniya so starshimi chastnymi proizvodnymi, Kazansk. matem. o-vo, Kazan, 2001, 226 pp.

[7] Copson E. T., “On the Riemann-Green fonction”, J. Rat. Mech. Anal., 1 (1958), 324–348 | DOI | MR | Zbl

[8] Volkodavov V. F., Nikolaev N. Ya., Bystrova O. K., Zakharov V. N., Funktsii Rimana dlya nekotorykh differentsialnykh uravnenii v $n$-mernom evklidovom prostranstve i ikh primeneniya, “Samarskii universitet”, Samara, 1995, 76 pp.

[9] Zhegalov V. I., “K sluchayam razreshimosti giperbolicheskikh uravnenii v terminakh spetsialnykh funktsii”, Neklassicheskie uravneniya matematicheskoi fiziki, Institut matematiki im. S. L. Soboleva SO RAN, Novosibirsk, 2002, 73–79 | Zbl

[10] Beitman G., Erdein A., Vysshie transtsendentnye funktsii, Nauka, M., 1973, 294 pp.

[11] Stepanov V. V., Kurs differentsialnykh uravnenii, GIFML, M., 1959, 468 pp.

[12] Zhegalov V. I., Sevastyanov V. A., “Zadacha Gursa v chetyrekhmernom prostranstve”, Differents. uravneniya, 32:10 (1996), 1429–1430 | MR | Zbl