Some extensions of Thomas-Fermi theory

Benilan, Ph. and H. Brezis, The Thomas-Fermi problem, in preparation.
Google Scholar
Benilan, Ph., H. Brezis, and M. G. Crandall, A semilinear elliptic equation in L¹ (ℝ^N), Ann. Scuola Norm. Sup. Pisa 2(1975), 523–555.
MathSciNet MATH Google Scholar
Brezis, H., Nonlinear problems related to the Thomas-Fermi equation, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations (ed. by G. M. de la Penha and L. A. Medieros), North-Holland, Amsterdam (1978), 81–89.
Google Scholar
Brezis, H., Some variational problems of Thomas-Fermi type, in Variational Inequalities and Complementary Problems: Theory and Applications (ed. by R. W. Cottle, F. Giannessi, and J.-L. Lions), Wiley, New York (1980), 53–73.
Google Scholar
Dyson, F. J. and A. Lenard, Stability of Matter, I, J. Math. Phys. 8 (1967), 423–434.
Article MathSciNet MATH Google Scholar
Fefferman, C. L., The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129–206.
Article MathSciNet MATH Google Scholar
Fermi, E., Un metodo statistico per la determinazione di alcune prioretà dell'atome, Rend. Acad. Naz. Lincei 6 (1927), 602–607.
Google Scholar
Gallouët, Th. and J.-M. Morel, Resolution of a semilinear equation in L¹, Proc. Roy. Soc. Edinburgh 96A (1984), 275–288 and 99A (1985), 399.
Article MATH Google Scholar
Gallouët, Th. and J.-M. Morel, On some semilinear problems in L¹, Boll. Un. Mat. Ital. 4A (1985), 123–131.
MATH Google Scholar
Lenard, A. and F. J. Dyson, Stability of matter, II, J. Math. Phys. 9 (1968), 698–711.
Article MathSciNet MATH Google Scholar
Lieb, E. H., The stability of matter, Rev. Mod. Phys. 48 (1976), 553–569.
Article MathSciNet Google Scholar
Lieb, E. H., Thomas-Fermi theory and related theories of atoms and molecules, Rev. Mod. Phys. 53 (1981), 603–641.
Article MathSciNet MATH Google Scholar
Lieb, E. H. and B. Simon, Thomas-Fermi theory revisited, Phys. Rev. Lett. 33 (1973), 681–683.
Article Google Scholar
Lieb, E. H. and B. Simon, The Thomas-Fermi theory of atoms, molecules and solids, Adv. Math. 23 (1977), 22–116.
Article MathSciNet MATH Google Scholar
Lieb, E. H. and W. E. Thirring, A bound for the kinetic energy of fermions which proves the stability of matter, Phys. Rev. Lett. 35 (1975), 687–689 and 1116.
Article Google Scholar
Rieder, G. R., Mathematical Contributions to Thomas-Fermi Theory, Ph.D. Thesis, Tulane University, New Orleans, 1986.
MATH Google Scholar
Thomas, L. H., The calculation of atomic fields, Proc. Camb. Phil. Soc. 23 (1927), 542–548.
Article MATH Google Scholar

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Department of Mathematics and Quantum Theory Group, Tulane University, 70118, New Orleans, LA, USA
Jerome A. Goldstein & Gisèle Ruiz Rieder

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Jerome A. Goldstein
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Gisèle Ruiz Rieder
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Angelo Favini Enrico Obrecht

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Goldstein, J.A., Rieder, G.R. (1986). Some extensions of Thomas-Fermi theory. In: Favini, A., Obrecht, E. (eds) Differential Equations in Banach Spaces. Lecture Notes in Mathematics, vol 1223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099187

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DOI: https://doi.org/10.1007/BFb0099187
Published: 15 November 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17191-1
Online ISBN: 978-3-540-47350-3
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