Comportement asymptotique des valeurs propres du laplacien dans un domaine avec un trou

Gérard Besson

Bulletin de la Société Mathématique de France (1985)

  • Volume: 113, page 211-230
  • ISSN: 0037-9484

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Besson, Gérard. "Comportement asymptotique des valeurs propres du laplacien dans un domaine avec un trou." Bulletin de la Société Mathématique de France 113 (1985): 211-230. <http://eudml.org/doc/87481>.

@article{Besson1985,
author = {Besson, Gérard},
journal = {Bulletin de la Société Mathématique de France},
keywords = {eigenvalues of the Laplace-Beltrami operator},
language = {fre},
pages = {211-230},
publisher = {Société mathématique de France},
title = {Comportement asymptotique des valeurs propres du laplacien dans un domaine avec un trou},
url = {http://eudml.org/doc/87481},
volume = {113},
year = {1985},
}

TY - JOUR
AU - Besson, Gérard
TI - Comportement asymptotique des valeurs propres du laplacien dans un domaine avec un trou
JO - Bulletin de la Société Mathématique de France
PY - 1985
PB - Société mathématique de France
VL - 113
SP - 211
EP - 230
LA - fre
KW - eigenvalues of the Laplace-Beltrami operator
UR - http://eudml.org/doc/87481
ER -

References

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  1. [A] AUBIN (T.), Nonlinear Analysis on Manifolds. Monge-Ampère equations, Grundlehren der Mathematischen Wissenschaften, 252, Springer-Verlag. Zbl0512.53044
  2. [B-G] BÉRARD (P.) et GALLOT (S.), C. R. Acad. Sc., t. 297, n° 3, p. 185-188. MR84k:58214
  3. [CV] COLIN DE VERDIÈRE (Y.), Pseudo-Laplacien I. Annales de l'Institut Fourier de Grenoble, t. 32, fasc. 3, 1982, p. 275-286. Zbl0489.58034MR84k:58221
  4. [C-F] CHAVEL (I.) and FELDMAN (E.), Spectra of domain in compact manifold, J. Funct. Anal., vol. 30, n° 2, 1978, p. 198-222. Zbl0392.58016MR80c:58027
  5. [D] DAHLANE (A.), Thèse de 3e cycle, Institut Fourier, Université de Grenoble-I. 
  6. [K] KLINGENBERG (W.), A course in differential geometry, Graduate texts in mathematics, 51, Springer-Verlag. Zbl0366.53001MR57 #13702
  7. [M-N-P] MAZUA (V. G.), NAZAROV (S.) and PLAMENEVSKII (F. A.), Math. U.S.S.R. Sbornik, vol. 44, n° 2, 1983, p. 167-194. Zbl0502.35017
  8. [R-S] REED (M.) and SIMON (B.), Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York, 1972. Zbl0242.46001MR58 #12429a
  9. [R-T] RAUCH (J.) and TAYLOR (M.), Potential and scattering theory on widly perturbed domain, J. Funct. Anal., vol. 18, 1975, p. 27-29. Zbl0293.35056MR51 #13476
  10. [O 1] OZAWA (S.), Surgery of domain and the Green's function of the Laplacian, Proc. Japan, Acad., vol. 56 A, 1980, p. 459-461. Zbl0468.35033MR82c:58056
  11. [O 2] OZAWA (S.), Singular Hadamard's variation of domains and eigenvalues of the Laplacian, Ibid., vol. 56 A, 1980, p. 306-310. Zbl0483.35063MR83g:49062a
  12. [O 3] OZAWA (S.), Singular variation of domains and eigenvalues of the Laplacian, Ibid., vol. 57 A, n 5, 1981, p. 242-246. Zbl0509.35060MR83g:49062b
  13. [O 4] OZAWA (S.), Singular variation of domains and eigenvalues of the Laplacian, Duke mathematical journal, vol. 48, 1981, p. 767-778. Zbl0483.35064MR86k:35117
  14. [O 5] OZAWA (S.), Singular Hadamard Variation 2, Proc. Japan Acad., vol. 57 A, 1981. Zbl0509.35060MR83g:49062b
  15. [O 6] OZAWA (S.), An asymptotic formula for the eigenvalues of the Laplacian in a Domain with a small hole, Ibid., vol. 58 A, 1982. Zbl0516.35015MR83j:58117

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