Geodesic
Asymptotics of negative eigenvalues of the Dirichlet problem with the density changing sign
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 27 (2009) no. 27, pp. 235-275 Cet article a éte moissonné depuis la source Math-Net.Ru

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S. A. Nazarov. Asymptotics of negative eigenvalues of the Dirichlet problem with the density changing sign. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 27 (2009) no. 27, pp. 235-275. http://geodesic.mathdoc.fr/item/TSP_2009_27_27_a6/

[1] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[2] Birman M. Sh., Solomyak M. Z., Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, Izd-vo Leningr. un-ta, L., 1980 | MR

[3] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[4] Vainberg M. M., Trenogin V. A., Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969 | MR

[5] Vishik M. I., Lyusternik L. A., “Regulyarnoe vyrozhdenie i pogranichnyi sloi dlya lineinykh differentsialnykh uravnenii s malym parametrom”, UMN, 12:5 (1957), 3–122 | MR | Zbl

[6] Nazarov S. A., “Obosnovanie asimptoticheskikh razlozhenii sobstvennykh chisel nesamosopryazhennykh singulyarno vozmuschennykh ellipticheskikh kraevykh zadach”, Mat. sb., 129:3 (1986), 307–337 | MR

[7] Mazya V. G., Nazarov S. A., Plamenevskii B. A., Asimptotika reshenii ellipticheskikh kraevykh zadach pri singulyarnom vozmuschenii oblasti, Izd-vo TGU, Tbilisi, 1981 | Zbl

[8] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[9] Nazarov S. A., Asimptoticheskaya teoriya tonkikh plastin i sterzhnei. Ponizhenie razmernosti i integralnye otsenki, Nauch. kniga, Novosibirsk, 2001

[10] Nazarov S. A., “Ravnomernye otsenki ostatkov v asimptoticheskikh razlozheniyakh reshenii zadachi o sobstvennykh kolebaniyakh pezoelektricheskoi plastiny”, Problemy mat. analiza, 25, Nauch. kniga, Novosibirsk, 2003, 99–188

[11] Lobo M., Nazarov S. A., Perez E., “Eigen-oscillations of contrasting non-homogeneous bodies: Asymptotic and uniform estimates for eigenvalues”, IMA J. Appl. Math., 70 (2005), 419–458 | DOI | MR | Zbl

[12] Gomez D., Lobo M., Nazarov S. A., Perez E., “Spectral stiff problems in domains surrounded by thin bands: Asymptotic and uniform estimates for eigenvalues”, J. Math. Pures Appl., 85 (2006), 598–632 | DOI | MR | Zbl

[13] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. MMO, 16 (1963), 219–292

[14] Nazarov S. A., Plamenevskii B. A., Ellipticheskie zadachi v oblastyakh s kusochno-gladkoi granitsei, Nauka, M., 1991

[15] Nazarov S. A., “Metod M. I. Vishika–L. A. Lyusternika v oblastyakh s konicheskimi tochkami”, DAN SSSR, 245:6 (1979), 1307–1311 | MR | Zbl

[16] Nazarov S. A., “Metod Vishika–Lyusternika dlya ellipticheskikh kraevykh zadach v oblastyakh s konicheskimi tochkami. 1. Zadacha v konuse”, Sib. mat. zhurn., 22:4 (1981), 142–163 | MR | Zbl

[17] Nazarov S. A., “Metod Vishika–Lyusternika dlya ellipticheskikh kraevykh zadach v oblastyakh s konicheskimi tochkami. 2. Zadacha v ogranichennoi oblasti”, Sib. mat. zhurn., 22:5 (1981), 132–152 | MR | Zbl

[18] Kamotskii I. V., Nazarov S. A., “O sobstvennykh funktsiyakh, lokalizovannykh okolo kromki tonkoi oblasti”, Problemy mat. analiza, 19, Nauch. kniga, Novosibirsk, 1999, 105–148

[19] Nazarov S. A., “Localization effects for eigenfunctions near to the edge of a thin domain”, Math. Bohem., 127:2 (2002), 283–292 | MR | Zbl

[20] Pérez E., “Remarks on vibrating systems with many concentrated masses and vibrating systems with parts of negligible mass”, Proc. Midnight Sun Narvik Conference. Multi Scale Problems and Asymptotic Analysis, Gakkuto Int. Ser., Gakkotosho, Tokyo, 2006, 311–323 | MR | Zbl

[21] Melnik T. A., Nazarov S. A., “Asimptoticheskaya struktura spektra v zadache o garmonicheskikh kolebaniyakh stupitsy s tyazhelymi spitsami”, Dokl. RAN, 333:1 (1993), 13–15 | MR | Zbl

[22] Melnik T. A., Nazarov S. A., “Asimptotika sobstvennykh znachenii zadachi Neimana v oblasti tipa «gustogo grebeshka»”, Dokl. RAN, 342:1 (1995), 23–25 | MR | Zbl

[23] Melnik T. A., Nazarov S. A., “Asimptotika resheniya spektralnoi zadachi Neimana v oblasti tipa «gustogo grebeshka»”, Tr. seminara im. I. G. Petrovskogo, 19 (1997), 138–173 | MR

[24] Melnik T. A., Nazarov S. A., “Asimptoticheskii analiz zadachi Neimana na soedinenii tela s tonkimi tyazhelymi sterzhnyami”, Algebra i analiz, 12:2 (2000), 188–238 | MR