On Lichtenstein's analysis of rotating newtonian stars

U. Heilig

Annales de l'I.H.P. Physique théorique (1994)

  • Volume: 60, Issue: 4, page 457-487
  • ISSN: 0246-0211

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Heilig, U.. "On Lichtenstein's analysis of rotating newtonian stars." Annales de l'I.H.P. Physique théorique 60.4 (1994): 457-487. <http://eudml.org/doc/76642>.

@article{Heilig1994,
author = {Heilig, U.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Euler's equation of a rigidly rotating body; implicit function theorem; existence},
language = {eng},
number = {4},
pages = {457-487},
publisher = {Gauthier-Villars},
title = {On Lichtenstein's analysis of rotating newtonian stars},
url = {http://eudml.org/doc/76642},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Heilig, U.
TI - On Lichtenstein's analysis of rotating newtonian stars
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 60
IS - 4
SP - 457
EP - 487
LA - eng
KW - Euler's equation of a rigidly rotating body; implicit function theorem; existence
UR - http://eudml.org/doc/76642
ER -

References

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  1. [1] J.F.G. Auchmuty and R. Beals, Variational Solutions of Some Nonlinear Free Boundary Problems, Arch. Rational Mech. Anal., Vol. 43, 1971, pp. 255-271. Zbl0225.49013MR337260
  2. [2] P.L. Lions, Minimization Problems in L1(R3), J. Funct. Anal., Vol. 41, 1981, pp. 236- 275. Zbl0464.49019MR615163
  3. [3] Y.Y. Li, On Uniformly Rotating Stars, Arch. Rational Mech. Anal., Vol. 115, 1991, pp. 367-393. Zbl0850.76784MR1120853
  4. [4] A. Liapounoff, Sur un problème de Tchebychef, Mémoires de l'Académie impériale des sciences de St-Petersbourg, Vol. 17 (8), 3, 1905, pp. 1-31. JFM37.0973.03
  5. [5] H. Poincaré, Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation, Acta Math., Vol. 7, 1885, pp. 259-380. JFM17.0864.02
  6. [6] A. Liapounoff, Sur les figures d'équilibre peu différentes des ellipsoides d'une masse liquide homogène, douée d'un mouvement de rotation. Première partie. Étude générale du problème, Mémoire présenté à l'Académie impériale des sciences, 1096, pp. 1-225. Zbl37.0718.13JFM37.0718.13
  7. [7] L. Lichtenstein, Untersuchung über die Gleichgewichtsfiguren rotierender Flüssigkeiten, deren Teilchen einander nach dem Newtonschen Gesetze anziehen. Erste Abhandlung. Homogene Flüssigkeiten. Allgemeine Existenzsätz, Math. Z., Vol. 1, 1918, pp. 229-284. Zbl46.1401.01MR1544295JFM46.1401.01
  8. [8] L. Lichtenstein, Untersuchung über die Gleichgewichtsfiguren rotierender Flüssigkeiten, deren Teilchen einander nach dem Newtonschen Gesetze anziehen. Dritte Abhandlung. Nichthomogene Flüssigkeiten. Figur der Erde, Math. Z., Vol. 36, 1933, pp. 481-562. Zbl0006.37305MR1545356JFM59.0752.05
  9. [9] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985, § 15. Zbl0559.47040MR787404
  10. [10] L. Lichtenstein, Gleichgewichtsfiguren rotierender Flüssigkeiten, Springer-Verlag, Berlin, 1933, pp. 22-28. Zbl0007.18104
  11. [11] E.J. Mcshane, Integration, Princeton University Press, 1947. Zbl0033.05302MR82536
  12. [12] E. Kreyszig, Introductory Functional Analysis With Applications, John Wiley and Sons Inc., New York, 1978, § 8. Zbl0368.46014MR467220
  13. [13] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1977, § 4. Zbl0361.35003MR473443

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