On the Paneitz energy on standard three sphere
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 211-223.

We prove that the Paneitz energy on the standard three-sphere S 3 is bounded from below and extremal metrics must be conformally equivalent to the standard metric.

DOI : 10.1051/cocv:2004002
Classification : 58E11, 35G99
Mots-clés : Paneitz operator, symmetrization, extremal metric 
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     title = {On the {Paneitz} energy on standard three sphere},
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     pages = {211--223},
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Yang, Paul; Zhu, Meijun. On the Paneitz energy on standard three sphere. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 211-223. doi : 10.1051/cocv:2004002. http://www.numdam.org/articles/10.1051/cocv:2004002/

[1] A. Jun, C. Kai-Seng and W. Juncheng, Self-similar solutions for the anisotropic affine curve shortening problem. Calc. Var. Partial Differ. Equ. 13 (2001) 311-337. | MR | Zbl

[2] T. Branson, Differential operators canonically associated to a conformal structure. Math. Scand. 57 (1985) 293-345. | MR | Zbl

[3] Y.S. Choi and X. Xu, Nonlinear biharmonic equation with negative exponent. Preprint (1999).

[4] Z. Djadli, E. Hebey and M. Ledoux, Paneitz type operators and applications. Duke Math. J. 104 (2000) 129-169. | MR | Zbl

[5] C. Fefferman and R. Graham, Conformal Invariants, in Élie Cartan et les Mathématiques d'aujourd'hui, Asterisque (1985) 95-116. | Numdam | Zbl

[6] E. Hebey and F. Robert, Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients. Calc. Var. Partial Differ. Equ. 13 (2001) 491-517. | Zbl

[7] E. Hebey, Sharp Sobolev inequalities of second order. J. Geom. Anal. 13 (2003) 145-162. | MR | Zbl

[8] S. Paneitz, A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds. Preprint (1983).

[9] G. Talenti, Elliptic equations and rearrangements. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 (1976) 697-718. | Numdam | MR | Zbl

[10] J. Wei and X. Xu, Classification of solutions of higher order conformally invariant equations. Math. Ann. 313 (1999) 207-228. | MR | Zbl

[11] X. Xu and P. Yang, On a fourth order equation in 3-D, A tribute to J.L. Lions. ESAIM: COCV 8 (2002) 1029-1042. | Numdam | MR | Zbl

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