Geodesic
Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a~ball
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 527-546.

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

Polynomial solution to Dirihlet boundary value problem for the nonhomogeneous $3$-harmonic equation in a ball with polynomial right-hand side and polynomial boundary data is found.
Keywords: $3$-harmonic equation, harmonic polynomials, Dirihlet boundary value problem
Mots-clés : Almansi decomposition, polynomial solutions. 
@article{JSFU_2012_5_4_a9,
     author = {Valery V. Karachik},
     title = {Polynomial solutions to {Dirihlet} boundary value problem for the $3$-harmonic equation in a~ball},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {527--546},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a9/}
}
TY  - JOUR
AU  - Valery V. Karachik
TI  - Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a~ball
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2012
SP  - 527
EP  - 546
VL  - 5
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a9/
LA  - ru
ID  - JSFU_2012_5_4_a9
ER  - 
%0 Journal Article
%A Valery V. Karachik
%T Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a~ball
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2012
%P 527-546
%V 5
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a9/
%G ru
%F JSFU_2012_5_4_a9
Valery V. Karachik. Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a~ball. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 527-546. http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a9/

[1] E. Almansi, “Sull'integrazione dell'equazione differenziale $\Delta^{2n}u=0$”, Ann. Mat. Pura Appl. Ser. 3, 2 (1899), 1–51 | DOI | Zbl

[2] V. V. Karachik, “Ob odnom razlozhenii tipa Almansi”, Matematicheskie zametki, 83:3 (2008), 370–380 | DOI | MR | Zbl

[3] N. Nicolescu, “Probléme de l'analyticité par rapport á un opérateur linéaire”, Studia Math., 16 (1958), 353–363 | MR | Zbl

[4] V. V. Karachik, “Razlozheniya Almansi dlya nevyrozhdennykh operatorov vtorogo poryadka”, Vestnik YuUrGU, Seriya “Matematika. Mekhanika. Fizika”, 2010, no. 30, 4–12

[5] V. S. Vladimirov, Sbornik zadach po uravneniyam matematicheskoi fiziki, 3-e izd., ispravl., ed. V. S. Vladimirov, FIZMATLIT, M., 2001

[6] V. V. Karachik, “On one set of orthogonal harmonic polynomials”, Proceedings of American Mathematical Society, 126:12 (1998), 3513–3519 | DOI | MR | Zbl

[7] V. V. Karachik, N. A. Antropova, “O reshenii neodnorodnogo poligarmonicheskogo uravneniya i neodnorodnogo uravneniya Gelmgoltsa”, Differentsialnye uravneniya, 46:3 (2010), 384–395 | MR | Zbl

[8] V. V. Karachik, “Postroenie polinomialnykh reshenii nekotorykh kraevykh zadach dlya uravneniya Puassona”, ZhVMiMF, 51:9 (2011), 1674–1694 | MR

[9] V. V. Karachik, N. A. Antropova, “O polinomialnykh reshenii zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Sibirskii zhurnal industrialnoi matematiki, 15:2(50) (2012), 86–98

[10] V. V. Karachik, “Ob odnom predstavlenii analiticheskikh funktsii garmonicheskimi”, Matematicheskie trudy, 10:2 (2007), 142–162 | MR | Zbl

[11] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, Nauka, M., 1966 | MR

[12] V. V. Karachik, “Ob odnoi zadache dlya poligapmonicheskogo upavneniya v shape”, Sibirskii matematicheskii zhupnal, 32:5 (1991), 51–58 | MR | Zbl

[13] V. V. Karachik, “Metod postroeniya reshenii lineinykh obyknovennykh differentsialnykh uravnenii s postoyannymi koeffitsientami”, ZhVMiMF, 52:2 (2012), 237–252 | MR | Zbl