Geodesic
A priori estimate of solutions of one boundary-value problem in a strip for a higher-order degenerate elliptic equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 116-125.

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

Coercive a priori estimates of solutions of a Dirichlet-type boundary-value problem in a strip for a certain higher-order degenerate elliptic equation containing weighted derivatives of a special form up to the order $2m$ and ordinary partial derivatives up to the order $2k-1$ under the condition $2m>2k-1$ are proved. At the boundary of the strip, Dirichlet-type conditions are imposed. A coercive a priori estimate for solutions of the problem considered in special weighted Sobolev-type spaces is obtained.
Keywords: a priori estimate, degenerate elliptic equation, Sobolev weight space. 
@article{INTO_2019_173_a8,
     author = {V. V. Pankov and A. D. Baev and V. D. Kharchenko and A. A. Babaitsev},
     title = {A priori estimate of solutions of one boundary-value problem in a strip for a higher-order degenerate elliptic equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {116--125},
     publisher = {mathdoc},
     volume = {173},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_173_a8/}
}
TY  - JOUR
AU  - V. V. Pankov
AU  - A. D. Baev
AU  - V. D. Kharchenko
AU  - A. A. Babaitsev
TI  - A priori estimate of solutions of one boundary-value problem in a strip for a higher-order degenerate elliptic equation
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 116
EP  - 125
VL  - 173
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_173_a8/
LA  - ru
ID  - INTO_2019_173_a8
ER  - 
%0 Journal Article
%A V. V. Pankov
%A A. D. Baev
%A V. D. Kharchenko
%A A. A. Babaitsev
%T A priori estimate of solutions of one boundary-value problem in a strip for a higher-order degenerate elliptic equation
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 116-125
%V 173
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_173_a8/
%G ru
%F INTO_2019_173_a8
V. V. Pankov; A. D. Baev; V. D. Kharchenko; A. A. Babaitsev. A priori estimate of solutions of one boundary-value problem in a strip for a higher-order degenerate elliptic equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 116-125. http://geodesic.mathdoc.fr/item/INTO_2019_173_a8/

[1] Baev A. D., “Vyrozhdayuschiesya ellipticheskie uravneniya vysokogo poryadka i svyazannye s nimi psevdodifferentsialnye operatory”, Dokl. AN SSSR., 265:5 (1982), 1044–1046 | MR | Zbl

[2] Baev A. D., Kachestvennye metody teorii kraevykh zadach dlya vyrozhdayuschikhsya ellipticheskikh uravnenii, Voronezh. gos. un-t, Voronezh, 2008

[3] Baev A. D., “Ob obschikh kraevykh zadachakh v poluprostranstve dlya vyrozhdayuschikhsya ellipticheskikh uravnenii vysokogo poryadka”, Dokl. RAN., 422:6 (2008), 727–728 | Zbl

[4] Baev A. D., Buneev S. S., “Ob odnom klasse kraevykh zadach v polose dlya vyrozhdayuschikhsya ellipticheskikh uravnenii vysokogo poryadka”, Dokl. RAN., 448:1 (2013), 7–8 | DOI | Zbl

[5] Baev A. D., Buneev S. S., “Apriornaya otsenka reshenii odnoi kraevoi zadachi v polose dlya vyrozhdayuschegosya ellipticheskogo uravneniya vysokogo poryadka”, Vestn. Voronezh. gos. un-ta. Ser. Fiz. Mat., 2012, no. 1, 81–92 | Zbl

[6] Baev A. D., Pankov V. V., “O suschestvovanii reshenii odnogo klassa kraevykh zadach v polose dlya vyrozhdayuschikhsya ellipticheskikh uravnenii vysokogo poryadka”, Dokl. RAN., 475:5 (2017), 1–3

[7] Vishik M. I., Grushin V. V., “Kraevye zadachi dlya ellipticheskikh uravnenii, vyrozhdayuschikhsya na granitse oblasti”, Mat. sb., 80 (112):4 (1969), 455–491 | Zbl

[8] Vishik M. I., Grushin V. V., “Vyrozhdayuschiesya ellipticheskie differentsialnye i psevdodifferentsialnye operatory”, Usp. mat. nauk., 25:4 (1970), 29–56 | MR | Zbl

[9] Glushko V. P., Apriornye otsenki reshenii kraevykh zadach dlya odnogo klassa vyrozhdayuschikhsya ellipticheskikh uravnenii vysokogo poryadka, Dep. v VINITI 27.03.1979, No 1048, VGU, Voronezh, 1979

[10] Pankov V. V., Baev A. D., Kharchenko V. D., “Ob apriornoi otsenke reshenii kraevoi zadachi v polose dlya vyrozhdayuschegosya ellipticheskogo uravneniya vysokogo poryadka”, Vestn. Voronezh. gos. un-ta. Ser. Fiz. Mat., 2018, no. 4, 162–173