This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliographie
Th. AUBIN-Problèmes isopérimétriques et espaces de Sobolev, C.R. Acad. Sci. Paris, 280(1975), p. 279–281.
Th. AUBIN-Espaces de Sobolev sur les variétés riemanniennes, Bull. Sci. Math., 100(1976), p. 149–173.
Th. AUBIN-Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, Journ. Math. Pures et Appl., 55(1976), p. 269–296.
J.F. BARNES, H.J. BRASCAMP et E.H. LIEB-Lower bound for the ground state energy at the Schrödinger equation using the sharp form of Young’s inequality, dans [15], pages 83 à 90.
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.]
G.A. BLISS-An integral inequality, Journ. London Math. Soc., 5(1930), p. 40–46.
R. COURANT et D. HILBERT-Methods of mathematical Physics, volume 1, Interscience, 1953.
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.
G.H. HARDY, J.E. LITTLEWOOD et G. POLYA-Inequalities, Cambridge University Press, deuxième édition, 1952.
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.
T. KATO-Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc., 70(1951), p. 195–211.
E.H. LIEB-The stability of matter, Reviews of Modern Physics, 48(1976), p. 555–569.
E.H. LIEB et J.L. LEBOWITZ-The constitution of matter: existence of thermodynamics for systems composed of electrons and nuclei, Adv. Math., 9(1972), p. 316–398.
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.
E.H. LIEB, B. SIMON et A.S. WIGHTMAN (éditeurs)-Studies in Mathematical Physics (Essays in honor of Valentine Bargmann), Princeton University Press, 1976.
J. MILNOR-Morse theory, Annals of Math. Studies, vol. 51, Princeton University Press, 1963.
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.
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.
J. SCHWINGER-On the bound states of a given potential, Proc. Nat. Acad. Sci. U.S.A., 47(1961), p. 122–129.
B. SIMON-On the number of bound states of two-body Schrödinger operators-a review, dans [15], paper 305 à 326.
B. SIMON-Quantum mechanics for hamiltonians defined by quadratic forms, Princeton University Press, 1971.
S. SOBOLEV-Sur un théorème d’Analyse Fonctionnelle, Mat. Sbornik, 46(1938), p. 471–496.
S. SOBOLEV-Sur les équations aux dérivées partielles hyperboliques non-linéaires, Edizioni Cremonese, Roma, 1961.
E. STEIN-Singular integrals and differentiability properties of functions, Princeton University Press, 1970.
Rights and permissions
Copyright information
© 1978 N. Bourbaki
About this paper
Cite this paper
Cartier, P. (1978). Spectre de l’équation de schrödinger, application a la stabilité de la matière [d’après J. Lebowitz, E. Lieb, B. Simon et W. Thirring]. In: Séminaire Bourbaki vol. 1976/77 Exposés 489–506. Lecture Notes in Mathematics, vol 677. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070756
Download citation
DOI: https://doi.org/10.1007/BFb0070756
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08937-7
Online ISBN: 978-3-540-35719-3
eBook Packages: Springer Book Archive
