Spectre de l'équation de Schrödinger, application à la stabilité de la matière

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1. [1] Th. Aubin - Problèmes isopérimétriques et espaces de Sobolev, C.R. Acad. Sci. Paris, 280(1975), p. 279-281. Zbl0295.53024MR407905
2. [2] Th. Aubin - Espaces de Sobolev sur les variétés riemanniennes, Bull. Sci. Math., 100(1976), p. 149-173. Zbl0328.46030MR488125
3. [3] Th. Aubin - Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, Journ. Math. Pures et Appl., 55(1976), p. 269-296. Zbl0336.53033MR431287
4. [4] J.F. Barnes , H.J. Brascamp et E.H. Lieb - Lower bound for the ground state energy of the Schrödinger equation using the sharp form of Young's inequality, dans [15] , pages 83 à 90. Zbl0354.35028
5. [5] M.S. Birman - Mat. Sbornik, 55(1961), p. 125-174 [Traduction anglaise: The spectrum of singular boundary value problems, Amer. Math. Soc. Translations, Series 2, 53(1966), p. 23-80. ] Zbl0174.42502MR142896
6. [6] G.A. Bliss - An integral inequality, Journ. London Math. Soc., 5(1930), p. 40-46. JFM56.0434.02
7. [7] R. Courant et D. Hilbert - Methods of mathematical Physics, volume 1, Interscience, 1953. Zbl0051.28802MR65391
8. [8] F.J. Dyson et A. Lenard - Stability of matter I : Journ. Math. Phys., 8(1967), p. 423-434, et II : ibid., 9(1968), p. 698-711. Zbl0948.81665
9. [9] G.H. Hardy , J.E. Littlewood et G. Polya - Inequalities, Cambridge University Press, deuxième édition, 1952. MR46395JFM60.0169.01
10. [10] V. Glaser , A. Martin , H. Grosse et W.E. Thirring - A family of optimal conditions for the absence of bound states in a potential, dans [15] , pages 169 à 194. Zbl0332.31004
11. [11] T. Kato - Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc., 70(1951),p. 195-211. Zbl0044.42701MR41010
12. [12] E.H. Lieb - The stability of matter, Reviews of Modern Physics, 48(1976), p. 555-569. MR456083
13. [13] E.H. Lieb et J.L. Lebowitz - The constitution of matter : existence of thermo-dynamics for systems composed of electrons and nuclei, Adv. Math., 9(1972), p. 316-398. Zbl1049.82501MR339751
14. [14] E.H. Lieb et W.E. Thirring - Inequalities for the moments of eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities, dans [15], pages 169 à 194. Zbl0342.35044
15. [15] E.H. Lieb , B. Simon et A.S. Wightman (éditeurs) - Studies in Mathematical Physics (Essays in honor of Valentine Bargmann), PrincetonUniversity Press, 1976. Zbl0326.00007
16. [16] J. Milnor - Morse theory, Annals of Math. Studies, vol. 51, Princeton UniversityPress, 1963. Zbl0108.10401MR163331
17. [17] G.D. Mostow - Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Publ. Math. I.H.E.S., 34(1968), p. 53-104. Zbl0189.09402MR236383
18. [18] G. Rosen - Minimum value for c in the Sobolev inequality ∥Φ3∥ ≤ c ∥∇Φ∥3, S.I.A.M. Journ. Appl. Math., 21(1971), p. 30-32. Zbl0201.38704
19. [19] J. Schwinger - On the bound states of a given potential, Proc. Nat. Acad. Sci. U.S.A., 47(1961), p. 122-129. MR129798
20. [20] B. Simon - On the number of bound states of two-body Schrödinger operators -- a review, dans [15] , pages 305 à 326. Zbl0349.35022
21. [21] B. Simon - Quantum mechanics for hamiltonians defined by quadratic forms, Princeton University Press, 1971. Zbl0232.47053MR455975
22. [22] S. Sobolev - Sur un théorème d'Analyse Fonctionnelle, Mat. Sbornik, 46(1938), p. 471-496. Zbl64.1100.02JFM64.1100.02
23. [23] S. Sobolev - Sur les équations aux dérivées partielles hyperboliques non-linéaires, Edizioni Cremonese, Roma, 1961. Zbl0115.08301MR185276
24. [24] E. Stein - Singular integrals and differentiability properties of functions, PrincetonUniversity Press, 1970. Zbl0207.13501MR290095