Peut-on entendre les trous d'un tambour ?

 Access to full text

 Full (PDF)

1. [Ae 1] C. ANNÉ. - Perturbation du spectre S TUBɛY (Conditions de Neumann), Séminaire de Théorie Spectrale et Géométrie, n° 4, Grenoble, rm 1985" 1986. Zbl1002.58508MR1046060
2. [Ae 2] C. ANNÉ. - Spectre du Laplacien et limite de variété avec perte de dimension, Preprint Institut Fourier, Grenoble, n° 45, 1985. MR1046060
3. [An] ANCONA. - Théorie du potentiel, Cours de 3ème cycle , Univ. Paris VI. 
4. [Au] T. AUBIN. - Non linear analysis on manifolds, Monge-Ampère equation. Springer Verlag Berlin, 1982. Zbl0512.53044MR681859
5. [Ba] C. BANDLE. - Isoperimetric inequalities and applications, Pitman London, 1980. Zbl0436.35063MR572958
6. [Bd] P.H. BÉRARD. - Spectral geometry : direct and inverse problems, Lecture Notes in Math. Springer 1207, 1986. Zbl0608.58001MR861271
7. [Bn] G. BESSON. - Comportement asymptotique des valeurs propres du laplacien dans un domaine avec un trou, Bull. Soc. Math. France , 113 ( 1985), 211-230. Zbl0577.58033MR820320
8. [Cl] I. CHAVEL. - Eigenvalue in riemannian geometry, Academic Press, New-York, 1984. Zbl0551.53001MR768584
9. [C-F 1] I. CHAVEL, E.A. FELDMAN. - Spectra of domains in compact manifolds, J. Funct. Anal., 30 ( 1978), 198-222. Zbl0392.58016MR515225
10. [C-F 2] I. CHAVEL, E.A. FELDMAN. - The Lenz shift and Wiener Sausage in insulated domains, Warwick Symposium on Stochastic Analysis, 1987. Zbl0616.60076MR894522
11. [C-F 3] I. CHAVEL, E.A. FELDMAN. - The Lenz shift and Wiener Sausage in riemannian manifolds, Compositio Math., 60 ( 1986), 65-84. Zbl0607.60066MR867957
12. [C-F 4] I. CHAVEL, E.A. FELDMAN. - Spectra of manifolds less a small hole, preprint, New-York, 1986. 
13. [C-P] J. CHAZARAIN, A. PIRIOU. - Introduction à la théorie des équations aux dérivées partielles, Gauthier-Villars, Paris, 1981. Zbl0446.35001MR598467
14. [Ck] G. CHOQUET. - Lecture on analysis, vol. 1, Benjamin New-York, 1969. 
15. [C-C] B. COLBOIS, Y. COLIN DE VERDIÈRE. - Sur la multiplicité de la première valeur propre d'une surface de Riemann à courbure constante. Prépublication de l'Institut Fourier n° 62, Grenoble , 1986. Zbl0656.53043
16. [C-H] R. COURANT, D. HILBERT. - Methods of Mathematical physics, Wiley-Interscience I 1953, II, 1962. Zbl0051.28802MR65391
17. [Cs 1] G. COURTOIS. - Estimations du noyau de l'opérateur de la chaleur et du noyau de Green d'une variété riemannienne, application aux variétés privées d'un ɛ-tube, C. R. Acad. Sci. Sér. I Math., 303 ( 1986), 135-138. Zbl0588.53030MR853604
18. [Cs 2] G. COURTOIS. - Spectre des variétés privées d'un ɛ-tube, Prépublication de l'Institut Fourier n° 61, Grenoble , 1986. MR1046061
19. [Cs 3] G. COURTOIS. - Comportement d'une variété riemannienne compacte sous perturbation topologique par excision d'un domaine. Thèse - Grenoble, 1987. 
20. [DG] G. DEL GROSSO, F. MARCHETTI. - Asymptotic estimates for the principal eigenvalue of the Laplacian in a geodesie ball, Appl. Math. Optim., 10 ( 1983), 37-50. Zbl0546.35049MR701899
21. [G-T] S. GlLBARD, N.S. TRUDINGER. - Elliptic partial differential equations of second order, Springer Verlag Berlin, 1983. Zbl0562.35001MR737190
22. [G-P] V. GUILLEMIN, A. POLLACK. - Differential topology, Prentice Hall, Engle-wood Cliffs, New-Jersey, 1974. Zbl0361.57001MR348781
23. [H-K] E. HEINTZE , H. KARCHER. - A general comparison theorem with applications to volume estimâtes for submanifolds, Ann. Sci. École Norm. Sup., 11 ( 1978), 451-470. Zbl0416.53027MR533065
24. [Kc] M. KAC. - Probabilistic methods in some problems of scattering theory, Rocky Mountain J. Math., 4 ( 1974), 511-537. Zbl0314.47006MR510113
25. [Ko] T. KATO. - Perturbation theory for linear operators, Springer Verlag, 1966. Zbl0148.12601MR203473
26. [L-Y] P. Li, S.T. YAU. - Eigenvalues of a compact riemannian manifold, Proc. Sympos. Pure Math., ( 1980), 205-239. Zbl0441.58014MR573435
27. [M-T] T. MATSUZAWA, S. TANNO. - Estimates of the first eigenvalue of a big cup domain of a 2-sphere, Comp. Math., 47 ( 1982), 95-100. Zbl0498.53033MR668783
28. [M-N-P] V.G. MAZ'YA, S.A. NAZAROV, B.A. PLAMENEVSKII. - Asympto-tic expansion of the eigenvalues of boundary value problems for the Laplace operator in domains with small holes, Math. U.S.S.R. Izv., 24 ( 1985), 321-345. Zbl0566.35031
29. [Ma] C. MIRANDA. - Partial differential equation of elliptic type, Springer Verlag Berlin, 1970. Zbl0198.14101MR284700
30. [Oz 1] S. OZAWA. - Singular Hadamard's variation of domains and eigenvalues of the Laplacian, Proc. Japan Acad. Ser. A Math.I, 56 ( 1980), 306-310; II 57 ( 1981), 242-246. Zbl0509.35060
31. [Oz 2] S. OZAWA. - Singular variation of domains and eigenvalues of the Laplacian, Duke Math. J., 48 ( 1981), 767-778. Zbl0483.35064MR782576
32. [Oz 3] S. OZAWA. - The Srst eigenvalues of the laplacian on two dimensional riemannian manifolds, Tohoku Math.J., 34 ( 1982), 7-14. Zbl0486.53035MR651702
33. [Oz 4] S. OZAWA. - Electrostatic capacity and eigenvalues of the Laplacian, J. Fac. Sci. Univ. Tokyo Sect IA Math., 30 ( 1982), 53-62. Zbl0531.35061MR700595
34. [Oz 5] S. OZAWA. - An asymptotic formula for the eigenvalues of the Laplacian in a three dimensional domain with a small hole, J. Fac. Sci. Univ. Tokyo Sect IA Math., 30 ( 1983), 243-247. Zbl0541.35060MR722496
35. [R-T] J. RAUCH, M. TAYLOR. - Potential and scattering on wildly perturbed domains, J. Funct. Anal., 18 ( 1975), 27-59. Zbl0293.35056MR377303
36. [Sr] F. SPITZER. - Electrostatic capacity, heat flow and Brownian motion, Z. Wahrsch. Verw. Gebiete, 3 ( 1964), 110-121. Zbl0126.33505MR172343