[Une inégalité de Sobolev optimale sur les varietés riemanniennes]
On présente des inégalités de Sobolev optimales sur les variétés riemanniennes. Ces inégalités contiennent un terme de courbure scalaire. Les démonstrations détaillées sont contenues dans [11].
We outline our results in [11] concerning some sharp Sobolev inequalities on Riemannian manifolds. Our inequalities emphasize the role of scalar curvature in this context.
Accepté le :
Publié le :
Yan Yan Li 1 ; Tonia Ricciardi 2
@article{CRMATH_2002__335_6_519_0, author = {Yan Yan Li and Tonia Ricciardi}, title = {A sharp {Sobolev} inequality on {Riemannian} manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {519--524}, publisher = {Elsevier}, volume = {335}, number = {6}, year = {2002}, doi = {10.1016/S1631-073X(02)02529-3}, language = {en}, }
Yan Yan Li; Tonia Ricciardi. A sharp Sobolev inequality on Riemannian manifolds. Comptes Rendus. Mathématique, Volume 335 (2002) no. 6, pp. 519-524. doi : 10.1016/S1631-073X(02)02529-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02529-3/
[1] Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geom., Volume 11 (1976), pp. 573-598
[2] Équations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. Pures Appl., Volume 55 (1976), pp. 269-296
[3] Some Nonlinear Problems in Riemannian Geometry, Springer-Verlag, New York, 1998
[4] The scalar-curvature problem on standard three-dimensional sphere, J. Funct. Anal., Volume 95 (1991), pp. 106-172
[5] Sobolev inequalities with remainder terms, J. Funct. Anal., Volume 62 (1985), pp. 73-86
[6] Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., Volume 36 (1983), pp. 437-477
[7] On the minimization of symmetric functionals, Rev. Math. Phys. (1994), pp. 1011-1032 (Special Issue)
[8] Sharp Sobolev inequalities with lower order remainder terms, Trans. Amer. Math. Soc., Volume 353 (2001), pp. 269-289
[9] Sharp constant in a Sobolev trace inequality, Indiana Univ. Math. J., Volume 37 (1988), pp. 687-698
[10] Meilleures constantes dans le théorème d'inclusion de Sobolev, Ann. Inst. H. Poincaré, Volume 13 (1996) no. 1, pp. 57-93
[11] Y.Y. Li, T. Ricciardi, A sharp Sobolev inequality on Riemannian manifolds, Preprint No. 3-2002, Dip. Mat. e Appl., Univ. of Naples Federico II
[12] Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries, Comm. Pure Appl. Math., Volume 50 (1997), pp. 449-487
[13] Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom., Volume 20 (1984), pp. 479-495
[14] Critical points of embeddings of H1,n0 into Orlicz spaces, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 5 (1988), pp. 425-464
[15] Best constant in Sobolev inequality, Ann. Mat. Pura Appl., Volume 110 (1976), pp. 353-372
Cité par Sources :
Commentaires - Politique