Elliptic equations with critical Sobolev exponents in dimension 3
Druet, Olivier
Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002), p. 125-142 / Harvested from Numdam
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@article{AIHPC_2002__19_2_125_0,
     author = {Druet, Olivier},
     title = {Elliptic equations with critical Sobolev exponents in dimension 3},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {19},
     year = {2002},
     pages = {125-142},
     mrnumber = {1902741},
     zbl = {1011.35060},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2002__19_2_125_0}
}

Druet, Olivier. Elliptic equations with critical Sobolev exponents in dimension 3. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) pp. 125-142. http://gdmltest.u-ga.fr/item/AIHPC_2002__19_2_125_0/

[1] Atkinson F.V., Peletier L.A., Elliptic equations with nearly critical growth, J. Differential Equations 70 (1987) 349-365. | MR 915493 | Zbl 0657.35058

[2] Aubin T., Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geom. 11 (1976) 573-598. | MR 448404 | Zbl 0371.46011

[3] Brézis H., Elliptic equations with limiting Sobolev exponents. The impact of topology, Comm. Pure Appl. Math. 39 (1986) 17-39. | MR 861481 | Zbl 0601.35043

[4] Brézis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983) 437-477. | MR 709644 | Zbl 0541.35029

[5] Brézis H., Peletier L.A., Asymptotics for elliptic equations involving critical Sobolev exponents, in: Modica L., Colombini F., Marino A., Spagnolo S. (Eds.), Partial Differential Equations and the Calculus of Variations, Birkhaüser, Basel, 1989. | MR 1034005 | Zbl 0685.35013

[6] Chang S.Y.A., Yang P.C., Compactness of isospectral conformal metrics in S3, Comment. Math. Helv. 64 (1989) 363-374. | MR 998854 | Zbl 0679.53038

[7] Druet O., The best constants problem in Sobolev inequalities, Math. Annalen 314 (1999) 327-346. | MR 1697448 | Zbl 0934.53028

[8] O. Druet, Optimal Sobolev inequalities and extremal functions, The three-dimensional case, Indiana University Mathematics Journal (to appear). | MR 1896157 | Zbl 1037.58012

[9] Druet O., Robert F., Asymptotic profile for the sub-extremals of the sharp Sobolev inequality on the sphere, Comm. PDE 26 (5-6) (2001) 743-778. | MR 1843283 | Zbl 0998.58010

[10] Gidas B., Ni W., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in Rn, in: Nachbin L. (Ed.), Mathematical Analysis and Applications, Academic Press, 1981, pp. 370-401. | MR 634248 | Zbl 0469.35052

[11] Gilbarg D., Trüdinger N., Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977. | MR 473443 | Zbl 1042.35002

[12] Han Z.C., Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. I.H.P., Analyse non-linéaire 8 (2) (1991) 159-174. | Numdam | MR 1096602 | Zbl 0729.35014

[13] Hebey E., Asymptotic behavior of positive solutions of quasilinear elliptic equations with critical Sobolev growth, J. Differential Integral Equations 13 (2000) 1073-1080. | MR 1775246 | Zbl 0976.35022

[14] Hebey E., Vaugon M., The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds, Duke Math. J. 79 (1995) 235-279. | MR 1340298 | Zbl 0839.53030

[15] Hebey E., Vaugon M., From best constants to critical functions, Math. Z. 237 (2001) 737-767. | MR 1854089 | Zbl 0992.58016

[16] Li Y.Y., Prescribing scalar curvature on Sn and related problems, part I, J. Differential Equations 120 (1995) 319-420. | MR 1347349 | Zbl 0827.53039

[17] Obata M., The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geom. 6 (1971) 247-258. | MR 303464 | Zbl 0236.53042

[18] Robert F., Asymptotic behaviour of a nonlinear elliptic equation with critical Sobolev exponent: the radial case, Adv. Differential Equations 6 (7) (2001) 821-846. | MR 1828998 | Zbl 1087.35026

[19] Schoen R., Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984) 479-495. | MR 788292 | Zbl 0576.53028

[20] Schoen R., Zhang D., Prescribed scalar curvature on the n-sphere, Calc. Var. PDE 4 (1996) 1-25. | MR 1379191 | Zbl 0843.53037

[21] Struwe M., A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z. 187 (1984) 511-517. | MR 760051 | Zbl 0535.35025

[22] Talenti G., Best constants in Sobolev inequality, Ann. Math. Pura Appl. 110 (1976) 353-372. | MR 463908 | Zbl 0353.46018