Geodesic
Multiple eigenvalues of the Laplace operator
Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 225-238 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Upper bounds are obtained for the multiplicities of the eigenvalues of the Laplace operator in a domain and on a manifold. Bibliography: 17 titles. 
@article{SM_1988_61_1_a16,
     author = {N. S. Nadirashvili},
     title = {Multiple eigenvalues of the {Laplace} operator},
     journal = {Sbornik. Mathematics},
     pages = {225--238},
     year = {1988},
     volume = {61},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_1_a16/}
}
TY  - JOUR
AU  - N. S. Nadirashvili
TI  - Multiple eigenvalues of the Laplace operator
JO  - Sbornik. Mathematics
PY  - 1988
SP  - 225
EP  - 238
VL  - 61
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1988_61_1_a16/
LA  - en
ID  - SM_1988_61_1_a16
ER  - 
%0 Journal Article
%A N. S. Nadirashvili
%T Multiple eigenvalues of the Laplace operator
%J Sbornik. Mathematics
%D 1988
%P 225-238
%V 61
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1988_61_1_a16/
%G en
%F SM_1988_61_1_a16
N. S. Nadirashvili. Multiple eigenvalues of the Laplace operator. Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 225-238. http://geodesic.mathdoc.fr/item/SM_1988_61_1_a16/

[1] Cheng S.-Y., “Eigenfunctions and Nodal Sets”, Comment. Math. Helvetici, 51:1 (1976), 43–55 | DOI | MR | Zbl

[2] Besson G., “Sur la Multiplicité de la Premier Valeur Propre des Surfaces Riemanniennes”, Ann. Inst. Fourier., 30:1 (1980), 109–128 | MR | Zbl

[3] Szego G., “Inequelities for Certain Eigenvalues of a Membrane of Given Area”, J. of Rat. Mech. Ann., 3 (1954), 343–356 | MR | Zbl

[4] Weinberger H. F., “An Isoperimetric inequality for the $n$-dimensional free membrane problem”, J. of Rat. Mech. Ann., 5 (1956), 633–636 | MR | Zbl

[5] Gromol D., Klingenberg V., Meier V., Rimanova geometriya v tselom, Mir, M., 1971

[6] Peetre J., “A generalization of Courant nodal line theorem”, Math. Scand., 5 (1957), 15–20 | MR | Zbl

[7] Yanke K., Emde F., Lesh F., Spetsialnye funktsii, Nauka, M., 1977

[8] Kurant R., Gilbert D., Metody matematicheskoi fiziki, T. 1, Gostekhizdat, M.-L., 1951

[9] Bers L., “Local behavior of solutions of general elliptic equations”, Comm. Pure Appi. Math., 8 (1955), 473–496 | DOI | MR | Zbl

[10] Hartman P., Wintner A., “On the local behavior of solutions of non-parabolic partial differential equations”, Amer. J. Math., 77 (1955), 453–493 | DOI | MR

[11] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya. Metody teorii gomologii, Nauka, M., 1984 | MR

[12] Landis E. M., “Nekotorye voprosy kachestvennoi teorii ellipticheskikh uravnenii vtorogo poryadka”, UMN, 18:1 (1963), 3–62 | MR | Zbl

[13] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, IL, M., 1957

[14] Berger M., Ganduchen P., Mazet E., “Le Spectra d'une Variété Riemanniene”, Lect. Notes Math., no. 194, 1971

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

[16] Brelo M., Osnovy klassicheskoi teorii potentsiala, Mir, M., 1964 | MR | Zbl

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