Geodesic
Spectral asymptotics of second-order degenerate elliptic operators
Izvestiya. Mathematics , Tome 8 (1974) no. 6, pp. 1343-1371.

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

The principal term of the spectral asymptotics is calculated for selfadjoint elliptic differential operators of second order having a strong power degeneracy on the boundary of the domain. 
@article{IM2_1974_8_6_a10,
     author = {I. L. Vulis and M. Z. Solomyak},
     title = {Spectral asymptotics of second-order degenerate elliptic operators},
     journal = {Izvestiya. Mathematics },
     pages = {1343--1371},
     publisher = {mathdoc},
     volume = {8},
     number = {6},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a10/}
}
TY  - JOUR
AU  - I. L. Vulis
AU  - M. Z. Solomyak
TI  - Spectral asymptotics of second-order degenerate elliptic operators
JO  - Izvestiya. Mathematics 
PY  - 1974
SP  - 1343
EP  - 1371
VL  - 8
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a10/
LA  - en
ID  - IM2_1974_8_6_a10
ER  - 
%0 Journal Article
%A I. L. Vulis
%A M. Z. Solomyak
%T Spectral asymptotics of second-order degenerate elliptic operators
%J Izvestiya. Mathematics 
%D 1974
%P 1343-1371
%V 8
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a10/
%G en
%F IM2_1974_8_6_a10
I. L. Vulis; M. Z. Solomyak. Spectral asymptotics of second-order degenerate elliptic operators. Izvestiya. Mathematics , Tome 8 (1974) no. 6, pp. 1343-1371. http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a10/

[1] Vishik M. I., “Kraevye zadachi dlya ellipticheskikh uravnenii, vyrozhdayuschikhsya na granitse oblasti”, Matem. sb., 35 (1954), 513–568 | Zbl

[2] Mikhlin S. G., “Vyrozhdayuschiesya ellipticheskie uravneniya”, Vestn. LGU, 1954, no. 8, 19–48

[3] Smirnov M. M., Vyrozhdayuschiesya ellipticheskie i giperbolicheskie uravneniya, Nauka, M., 1966 | MR

[4] Solomesch I. A., “O sobstvennykh chislakh nekotorykh vyrozhdayuschikhsya ellipticheskikh uravnenii”, Matem. sb., 54 (1961), 295–310 | Zbl

[5] Solomesch I. A., “Ob asimptotike sobstvennykh znachenii bilineinykh form, svyazannykh s nekotorymi vyrozhdayuschimisya na granitse ellipticheskimi uravneniyami”, Dokl. AN SSSR, 144 (1962), 727–729 | Zbl

[6] Baouendi M. S., Goulaouic C., “Regularity et theorie spectrale pour une classe d'opérateurs elliptiques dégénérés”, Arch. Rat. Mech. Anal., 34:5 (1969), 361–379 | DOI | MR | Zbl

[7] Goulaouic C., “Sur la theorie spectrale des operateurs elliptiques (eventuellement dégénérés),”, Lect. Notes Math., 179, 1971, 231–244

[8] Boutet de Monvel L., Grisvard P., “Le comportement asymptotique des valeurs propres d'un operateur”, Compt. Rend. Acad. Sci. Paris, 272:1 (1971), A23–A26

[9] El Kolli A., “$n_{{\rm }i\grave eme}$ épaisseur dans les espaces de Sobolev avec poids”, Compt. Rend. Acad. Sci. Paris, 273:111 (1971), A450–A453 | MR

[10] Tulovskii V. H., “Ob asimptoticheskom raspredelenii sobstvennykh chisel vyrozhdayuschikhsya ellipticheskikh uravnenii vtorogo poryadka”, Matem. sb., 86(128):1 (1971), 76–89 | MR | Zbl

[11] Goryunov A. F., “Asimptoticheskie formuly sobstvennykh znachenii ellipticheskikh operatorov vtorogo poryadka, vyrozhdayuschikhsya na osi tsilindra”, Diff. uravneniya, 6:11 (1970), 2041–2052 | Zbl

[12] Goryunov A. F., “K voprosu ob asimptoticheskom raspredelenii sobstvennykh znachenii vyrozhdayuschikhsya ellipticheskikh operatorov vtorogo poryadka”, Diff. uravneniya, 6:12 (1970), 2214–2223 | Zbl

[13] Birman M. Sh., Solomyak M. Z., “O glavnom chlene spektralnoi asimptotiki dlya negladkikh ellipticheskikh zadach”, Funkts. analiz, 4:4 (1970), 1–13 | MR | Zbl

[14] Birman M. Sh., Solomyak M. Z., “Ob asimptotike spektra negladkikh ellipticheskikh uravnenii”, Funkts. analiz, 5:1 (1971), 69–70 | MR | Zbl

[15] Birman M. Sh., Solomyak M. Z., “Spektralnaya asimptotika negladkikh ellipticheskikh operatorov”, Dokl. AN SSSR, 205 (1971), 267–270 | MR

[16] Birman M. Sh., Solomyak M. Z., “Spektralnaya asimptotika negladkikh ellipticheskikh operatorov, I”, Tr. Mosk. matem. ob-va, 27, 1972, 3–52 | MR | Zbl

[17] Shimakura N., “Quelques exemples des $\zeta$-fonctions d'Epstein pour les opérateurs elliptiques dégénérés du second ordre”, Proc. Japan Acad. Sci., 45:10 (1969), 866–871 | DOI | MR | Zbl

[18] Shimakura N., “Quelques exemples des $\zeta$-fonctions d'Epstein pour les opérateurs elliptiques dégénérés du second ordre, II”, Proc. Japan Acad. Sci., 46:10 (1970), 1065–1069 | DOI | MR | Zbl

[19] Kostyuchenko A. G., Levitan B. M., “Ob asimptoticheskom povedenii sobstvennykh znachenii operatornoi zadachi Shturma–Liuvillya”, Funkts. analiz, 1:1 (1967), 86–96 | Zbl

[20] Vulis I. L., Solomyak M. 3., “Spektralnaya asimptotika vyrozhdayuschikhsya ellipticheskikh operatorov”, Dokl. AN SSSR, 207 (1972), 262–265 | MR | Zbl

[21] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[22] Calderon A. P., “Lebesgue spaces of differentiable functions”, Conf. on partial diff. eq., Univ. of California, 1960 | Zbl

[23] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969 | MR

[24] Smirnov V. I., Kurs vysshei matematiki, t. IV, Gostekhizdat, M., 1957

[25] Nordin C., “The asymptotic distribution of the eigenvalues of a degenerate elliptic operator”, Arkiv för Matematik, 10:1 (1972), 9–21 | DOI | MR | Zbl

[26] Taschiyan G. M., “O raspredelenii sobstvennykh chisel ellipticheskoi zadachi Dirikhle”, Tr. 6-i Drogobychskoi shkoly-simpoziuma po matematicheskomu programmirovaniyu i smezhnym voprosam, sektsiya funktsionalnogo analiza, 1974, 273–289