General boundary value problems for a class of singular and degenerate elliptic equations
Sbornik. Mathematics, Tome 40 (1981) no. 3, pp. 325-347 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper investigates general boundary value problems for a class of singular and degenerate elliptic equations satisfying Lopatinskii-type conditions on the part of the boundary where the singularity is concentrated. In the elliptic equations considered, the singular Bessel operator $\displaystyle B=\frac{\partial^2}{\partial y^2}+\frac{2\nu+1}y\frac\partial{\partial y}$ operates on one of the variables. For the above-mentioned problems coercive (a priori) bounds are given, right and left regularizers are given, and, with these, Fredholm solvability is proved. Bibliography: 15 titles.
@article{SM_1981_40_3_a2,
     author = {V. V. Katrakhov},
     title = {General boundary value problems for a~class of singular and degenerate elliptic equations},
     journal = {Sbornik. Mathematics},
     pages = {325--347},
     year = {1981},
     volume = {40},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_40_3_a2/}
}
TY  - JOUR
AU  - V. V. Katrakhov
TI  - General boundary value problems for a class of singular and degenerate elliptic equations
JO  - Sbornik. Mathematics
PY  - 1981
SP  - 325
EP  - 347
VL  - 40
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1981_40_3_a2/
LA  - en
ID  - SM_1981_40_3_a2
ER  - 
%0 Journal Article
%A V. V. Katrakhov
%T General boundary value problems for a class of singular and degenerate elliptic equations
%J Sbornik. Mathematics
%D 1981
%P 325-347
%V 40
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1981_40_3_a2/
%G en
%F SM_1981_40_3_a2
V. V. Katrakhov. General boundary value problems for a class of singular and degenerate elliptic equations. Sbornik. Mathematics, Tome 40 (1981) no. 3, pp. 325-347. http://geodesic.mathdoc.fr/item/SM_1981_40_3_a2/

[1] M. V. Keldysh, “O nekotorykh sluchayakh vyrozhdeniya uravnenii ellipticheskogo tipa na granitse oblasti”, DAN SSSR, 77:2 (1951), 181–183

[2] A. V. Bitsadze, Uravneniya smeshannogo tipa, izd-vo AN SSSR, Moskva, 1959

[3] I. A. Kipriyanov, “Preobrazovaniya Fure–Besselya i teoremy vlozheniya dlya vesovykh klassov”, Trudy matem. in-ta im. V. A. Steklova, LXXXIX (1967), 130–213

[4] M. I. Vishik, V. V. Grushin, “Kraevye zadachi dlya ellipticheskikh uravnenii, vyrozhdayuschikhsya na granitse oblasti”, Matem. sb., 80(122) (1969), 455–491 | Zbl

[5] J. Delsarte, “Sur ccrtaines transformations fonctionnetles relative aux equations aux derivees partielles du second ordre”, C. r. Acad. Sci. Paris, 206 (1938), 1780 | Zbl

[6] J. L. Lions, “Operateurs de Delsarte et problemes mixtes”, Bull. Soc. Math., France, 84 (1956), 9–95 | MR | Zbl

[7] J. L. Lions, Equations differentiates et problémes aux limites, Springer-Verlag, Berlin, 1961 | MR | Zbl

[8] Zh.-L. Lions, E. Madzhenes, Neodnorodnye granichnye zadachi i ikh prilozheniya, izd-vo “Mir”, Moskva, 1971

[9] L. Khërmander, Lineinye differentsialnye operatory s chastnymi proizvodnymi, izd-vo “Mir”, Moskva, 1965 | MR

[10] R. Kurant, Uravneniya s chastnymi proizvodnymi, izd-vo “Mir”, Moskva, 1964 | MR

[11] I. A. Kipriyanov, V. V. Katrakhov, “Ob odnom klasse odnomernykh singulyarnykh psevdodifferentsialnykh operatorov”, Matem. sb., 104(146) (1977), 49–68 | Zbl

[12] V. V. Katrakhov, “Operatory preobrazovaniya i psevdodifferentsialnye operatory”, Sib. matem. zh., 21:1 (1980), 86–97 | MR | Zbl

[13] V. V. Katrakhov, Spektralnaya funktsiya nekotorykh singulyarnykh differentsialnykh operatorov, Diff. uravneniya, 12, no. 7, 1976 | MR | Zbl

[14] G. N. Vatson, Teoriya besselevykh funktsii, IL, Moskva, 1949

[15] V. V. Katrakhov, “Obschie kraevye zadachi dlya odnogo klassa singulyarnykh i vyrozhdayuschikhsya uravnenii”, DAN SSSR, 251:6 (1980) | MR