Geodesic
Asymptotics of the solutions of some higher order elliptic equations in conical domains
Sbornik. Mathematics, Tome 53 (1986) no. 1, pp. 89-117 
A. M. Il'in; E. F. Lelikova. Asymptotics of the solutions of some higher order elliptic equations in conical domains. Sbornik. Mathematics, Tome 53 (1986) no. 1, pp. 89-117. http://geodesic.mathdoc.fr/item/SM_1986_53_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the equation $((-1)^mP(D_x,D_y)+D_y)u=f$, where $P$ is a homogeneous positive polynomial of degree $2m$, $x\in\mathbf R^2$ and $y\in\mathbf R^1$, the first boundary value problem is considered in a conical domain. The asymptotics of the solution at infinity is studied under the condition that the right side and the boundary functions asymptotically coincide with polynomials. Bibliography: 7 titles.

[1] Ilin A. M., Lelikova E. F., “Asimptotika reshenii nekotorykh ellipticheskikh uravnenii v neogranichennykh oblastyakh”, Matem. sb., 119(161) (1982), 307–324 | MR | Zbl

[2] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi i uglovymi tochkami”, Tr. MMO, 16 (1967), 209–292 | Zbl

[3] Ilin A. M., Gorkoe Yu. P., Lelikova E. F., “Asimptotika resheniya ellipticheskogo uravneniya s malym parametrom pri starshikh proizvodnykh v okrestnosti osoboi kharakteristiki predelnogo uravneniya”, Tr. semin. im. I. G. Petrovskogo, I, 1975, 75–133 | Zbl

[4] Shaigardanov Yu. Z., “Ob asimptotike resheniya pervoi kraevoi zadachi dlya ellipticheskogo uravneniya chetvertogo poryadka s malym parametrom pri starshikh proizvodnykh”, Primenenie metoda soglasovaniya asimptoticheskikh razlozhenii k kraevym zadacham dlya differentsialnykh uravnenii, Sverdlovsk, 1979, 58–72 | MR

[5] Lelikova E. F., “Ob asimptotike resheniya ellipticheskogo uravneniya s malym parametrom v oblasti s kusochno gladkoi granitsei”, Primenenie metoda soglasovaniya asimptoticheskikh razlozhenii k kraevym zadacham dlya differentsialnykh uravnenii, Sverdlovsk, 1979, 10–57

[6] Lelikova E. F., “Asimptotika resheniya ellipticheskogo uravneniya s malym parametrom v oblasti s konicheskoi tochkoi”, Differents. uravneniya, 19:2 (1983), 305–318 | MR | Zbl

[7] Ilin A. M., “Ob asimptotike resheniya kraevoi zadachi na polupryamoi dlya odnogo parabolicheskogo uravneniya”, Primenenie metoda soglasovaniya asimptoticheskikh razlozhenii k kraevym zadacham dlya differentsialnykh uravnenii, Sverdlovsk, 1979, 81–92 | MR | Zbl