Comptes Rendus
Partial Differential Equations
A fully nonlinear version of the Yamabe problem and a Harnack type inequality
[Une version complètement nonlinéaire du problème de Yamabe et une inégalité du type Harnack]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 4, pp. 319-324.

On étudie une version complètement nonlinéaire du problème de Yamabe. On etablit aussi une inégalité du type Harnack pour des équations elliptiques de second ordre, complètement nonlinéaires, avec invariance conforme. Les démonstrations détaillées de ces résultats sont présentées ailleurs.

We present some results on a fully nonlinear version of the Yamabe problem and a Harnack type inequality for general conformally invariant fully nonlinear second order elliptic equations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00017-7

Aobing Li 1 ; Yan Yan Li 1

1 Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854, USA
@article{CRMATH_2003__336_4_319_0,
     author = {Aobing Li and Yan Yan Li},
     title = {A fully nonlinear version of the {Yamabe} problem and a {Harnack} type inequality},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {319--324},
     publisher = {Elsevier},
     volume = {336},
     number = {4},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00017-7},
     language = {en},
}
TY  - JOUR
AU  - Aobing Li
AU  - Yan Yan Li
TI  - A fully nonlinear version of the Yamabe problem and a Harnack type inequality
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 319
EP  - 324
VL  - 336
IS  - 4
PB  - Elsevier
DO  - 10.1016/S1631-073X(03)00017-7
LA  - en
ID  - CRMATH_2003__336_4_319_0
ER  - 
%0 Journal Article
%A Aobing Li
%A Yan Yan Li
%T A fully nonlinear version of the Yamabe problem and a Harnack type inequality
%J Comptes Rendus. Mathématique
%D 2003
%P 319-324
%V 336
%N 4
%I Elsevier
%R 10.1016/S1631-073X(03)00017-7
%G en
%F CRMATH_2003__336_4_319_0
Aobing Li; Yan Yan Li. A fully nonlinear version of the Yamabe problem and a Harnack type inequality. Comptes Rendus. Mathématique, Volume 336 (2003) no. 4, pp. 319-324. doi : 10.1016/S1631-073X(03)00017-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00017-7/

[1] L. Caffarelli; B. Gidas; J. Spruck Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math., Volume 42 (1989), pp. 271-297

[2] L. Caffarelli; L. Nirenberg; J. Spruck The Dirichlet problem for nonlinear second-order elliptic equations, III: Functions of the eigenvalues of the Hessian, Acta Math., Volume 155 (1985), pp. 261-301

[3] S.Y. A. Chang, M. Gursky, P. Yang, An a priori estimate for a fully nonlinear equation on four-manifolds, Preprint

[4] P. Guan, J. Viaclovsky, G. Wang, Some properties of the Schouten tensor and applications to conformal geometry, Preprint

[5] P. Guan, G. Wang, A fully nonlinear conformal flow on locally conformally flat manifolds, Preprint

[6] M. Gursky, J. Viaclovsky, A conformal invariant related to some fully nonlinear equations, Preprint

[7] A. Li; Y.Y. Li On some conformally invariant fully nonlinear equations, C. R. Acad. Sci. Paris Sér. I, Volume 334 (2002), pp. 1-6

[8] A. Li, Y.Y. Li, On some conformally invariant fully nonlinear equations, Preprint

[9] A. Li, Y.Y. Li, On some conformally invariant fully nonlinear elliptic operators, Part II: Liouville, Harnack and Yamabe, in preparation

[10] Y.Y. Li Degree theory for second order nonlinear elliptic operators and its applications, Comm. Partial Differential Equations, Volume 14 (1989), pp. 1541-1578

[11] Y.Y. Li, L. Zhang, Liouville type theorems and Harnack type inequalities for semilinear elliptic equations, J. Anal. Math., to appear

[12] R. Schoen Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom., Volume 20 (1984), pp. 479-495

[13] R. Schoen On the number of constant scalar curvature metrics in a conformal class (H.B. Lawson; K. Tenenblat, eds.), Differential Geometry: A symposium in honor of Manfredo Do Carmo, Wiley, 1991, pp. 311-320

[14] R. Schoen, Courses at Stanford University, 1988, and New York University, 1989

[15] R. Schoen; S.T. Yau Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math., Volume 92 (1988), pp. 47-71

[16] J. Viaclovsky, Estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds, Comm. Anal. Geom., to appear

[17] J. Viaclovsky Conformal geometry, contact geometry, and the calculus of variations, Duke Math. J., 101 (2000), pp. 283-316

Cité par Sources :

Commentaires - Politique