Meilleures constantes dans le théorème d'inclusion de Sobolev

Emmanuel Hebey; Michel Vaugon

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 1, page 57-93
  • ISSN: 0294-1449

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Hebey, Emmanuel, and Vaugon, Michel. "Meilleures constantes dans le théorème d'inclusion de Sobolev." Annales de l'I.H.P. Analyse non linéaire 13.1 (1996): 57-93. <http://eudml.org/doc/78376>.

@article{Hebey1996,
author = {Hebey, Emmanuel, Vaugon, Michel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {best constants; Sobolev imbedding theorem; locally conformally flat manifolds; points of concentration; blow-up},
language = {eng},
number = {1},
pages = {57-93},
publisher = {Gauthier-Villars},
title = {Meilleures constantes dans le théorème d'inclusion de Sobolev},
url = {http://eudml.org/doc/78376},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Hebey, Emmanuel
AU - Vaugon, Michel
TI - Meilleures constantes dans le théorème d'inclusion de Sobolev
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 1
SP - 57
EP - 93
LA - eng
KW - best constants; Sobolev imbedding theorem; locally conformally flat manifolds; points of concentration; blow-up
UR - http://eudml.org/doc/78376
ER -

References

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  1. [1] R.A. Adams, Sobolev spaces, Academic press, Pure and Applied Mathematics, vol. 65, 1978. Zbl0314.46030MR450957
  2. [2] T. Aubin, Nonlinear Analysis on Manifolds, Monge-Ampère equations, Berlin, Springer-Verlag, 1982, Grudlehern Math. Wiss., vol. 252. Zbl0512.53044MR681859
  3. [3] T. Aubin, Problèmes isopérimétriques et espace de Sobolev, Journal of Differential Geometry, vol. 11, 1976, p. 573-598. Zbl0371.46011MR448404
  4. [4] T. Aubin, Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, Journal de Mathématiques Pures et Appliquées, vol. 55, 1976, p. 269-296. Zbl0336.53033MR431287
  5. [5] A. Besse, Einstein manifolds, Springer-Verlag, vol. 10, 1987. Zbl0613.53001MR867684
  6. [6] H. Brezis, Elliptic equations with limiting Sobolev exponents, the impact of topology, Comm. Pure and Appl. Math., vol. XXXIX, 1986, p. 17-39. Zbl0601.35043MR861481
  7. [7] P. Cherrier, Meilleures constantes dans des inégalités relatives aux espaces de Sobolev, Bull. Sci. Math., vol. 108, 1984, p. 225-262. Zbl0547.58017MR771911
  8. [8] L.A. Caffarelli, B. Gidas et J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with Sobolev growth, Comm. Pure and Appl. Maths., vol. XLII, 1989, p. 271-297. Zbl0702.35085MR982351
  9. [9] S. Gallot, Inégalités isopérimétriques sur les variétés riemanniennes, Astérisques, 1988, p. 163-164. Zbl0674.53001
  10. [10] B. Gidas, W.M. Ni et L. Nirenberg, Symmetry and related properties via the maximum principle, Communications in Mathematical Physics, vol. 68, 1979, p. 209-243. Zbl0425.35020MR544879
  11. [11] D. Gilbarg et N.S. Trudinger, Elliptic partial differential equations of second order, Berlin, Springer-Verlag, Second edition, 1983, Grundleher Math. Wiss., vol. 224. Zbl0562.35001MR737190
  12. [12] Z.C. Han, Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Annales de l'Institut Henri Poincaré, Analyse non linéaire, vol. 8, 1991, p. 159-174. Zbl0729.35014MR1096602
  13. [13] E. Hebey, Changements de métriques conformes sur la sphère, Le problème de Nirenberg, Bull. Sc. Math., vol. 114, 1990, p. 215-242. Zbl0713.53023MR1056162
  14. [14] E. Hebey, La méthode d'isométries-concentration dans le cas d'un problème non linéaire sur la variétés riemanniennes compactes à bord avec exposant critique de Sobolev, Bull. Sc. Math., vol. 116, 1992, p. 35-51. Zbl0756.35028MR1154371
  15. [15] E. Hebey, Courbure scalaire et géométrie conforme, Journal of Geometry and Physics, vol. 10, 1993, p. 345-380. Zbl0785.53028MR1218556
  16. [16] E. Hebey et M. Vaugon, Meilleures constantes dans le théorème d'inclusion de Sobolev et multiplicité pour les problèmes de Nirenberg et Yamabe, Indiana University Mathematics Journal, vol. 41, 1992, p. 377-407. Zbl0764.53029MR1183349
  17. [17] S. Kobayashi et K. Nomizu, Foundations of differential geometry, Interscience tracts in pure and applied mathematics, n° 15, John Wiley & Sons. Zbl0119.37502
  18. [18] J.L. Kazdan et F.W. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., vol. 28, 1975, p. 567-597. Zbl0325.35038MR477445
  19. [19] P.L. Lions, The concentration-compactness principle in the calculus of variations, Rev. Math. Iberoamericano, vol. 1.1, 1985, p. 145-201, et vol. 1.2, 1985, p. 45-121. Zbl0704.49005MR850686
  20. [20] M. Obata, The conjectures on conformal transformations of riemannian manifolds, J. Diff. Geom., vol. 6, 1971, p. 247-258. Zbl0236.53042MR303464
  21. [21] M. Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z., vol. 187, 1984, p. 511-517. Zbl0535.35025MR760051
  22. [22] P. Sacks et K. Uhlenbeck, On the existence of minimal immersions of 2-sphères, Ann. of Math., vol. 113, 1981, p. 1-24. Zbl0462.58014MR604040
  23. [23] G. Talenti, Best constant in Sobolev inequality, Ann. Math. Pure Appl., vol. 110, 1976, p. 353-372. Zbl0353.46018MR463908
  24. [24] M. Vaugon, Transformation conforme de la courbure scalaire sur une variété riemannienne compacte, Journal of Functional Analysis, vol. 71, 1987, p. 182-194. Zbl0608.53041MR879707
  25. [25] H.C. Wente, Large solutions to the volume constrained Plateau problem, Arch. Rat. Mech. Anal., vol. 75, 1980, p. 59-77. Zbl0473.49029MR592104

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