Geodesic
Potential theory for the equation of small oscillations of a rotating fluid
Sbornik. Mathematics, Tome 37 (1980) no. 4, pp. 559-579 
B. V. Kapitonov. Potential theory for the equation of small oscillations of a rotating fluid. Sbornik. Mathematics, Tome 37 (1980) no. 4, pp. 559-579. http://geodesic.mathdoc.fr/item/SM_1980_37_4_a4/
@article{SM_1980_37_4_a4,
     author = {B. V. Kapitonov},
     title = {Potential theory for the equation of small oscillations of a~rotating fluid},
     journal = {Sbornik. Mathematics},
     pages = {559--579},
     year = {1980},
     volume = {37},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1980_37_4_a4/}
}
TY  - JOUR
AU  - B. V. Kapitonov
TI  - Potential theory for the equation of small oscillations of a rotating fluid
JO  - Sbornik. Mathematics
PY  - 1980
SP  - 559
EP  - 579
VL  - 37
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1980_37_4_a4/
LA  - en
ID  - SM_1980_37_4_a4
ER  - 
%0 Journal Article
%A B. V. Kapitonov
%T Potential theory for the equation of small oscillations of a rotating fluid
%J Sbornik. Mathematics
%D 1980
%P 559-579
%V 37
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1980_37_4_a4/
%G en
%F SM_1980_37_4_a4

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

With the aid of potential theory the classical solvability of initial-boundary value problems is proved for the equation $$ \frac{\partial^2}{\partial t^2}\biggl(\frac{\partial^2u}{\partial x_1^2}+\frac{\partial^2u}{\partial x_2^2}+\frac{\partial ^2u}{\partial x_3^2}\biggr)+\frac{\partial^2u}{\partial x_3^2}=0 $$ in a bounded domain of the space $\Omega$, and also in the complement of this domain. For the first boundary value problem a method of obtaining estimates of solutions in uniform norms is established, with an indication of the explicit dependence of the constants on the time exhibited. Bibliography: 6 titles.

[1] S. L. Sobolev, “Ob odnoi novoi zadache matematicheskoi fiziki”, Izv. AN SSSR, seriya matem., 18 (1954), 3–50 | MR | Zbl

[2] S. L. Sobolev, “Sur une classe des problémes des physique mathematique”, $48$ Riunione della Societa Italiana per il progresso delta Scienze, Roma, 1965, 192–208 | MR | Zbl

[3] T. I. Zelenyak, Izbrannye voprosy kachestvennoi teorii uravnenii s chastnymi proizvodnymi, izd-vo NGU, Novosibirsk, 1970

[4] B. V. Kapitonov, Asimptotika reshenii kraevykh zadach dlya uravneniya malykh kolebanii vraschayuscheisya zhidkosti, Kandidatskaya dissertatsiya, Novosibirsk, 1977 | Zbl

[5] N. M. Mikhailova-Gubenko, “Singulyarnye integralnye uravneniya v prostranstvakh Lipshitsa”, Vestnik LGU, 1966, no. 1, 51–63

[6] N. M. Gyunter, Teoriya potentsiala i ee primenenie k osnovnym zadacham matematicheskoi fiziki, Gostekhizdat, Moskva, 1953 | MR