# On a fourth order equation in 3-D

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 8, page 1029-1042
- ISSN: 1292-8119

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topXu, Xingwang, and Yang, Paul C.. "On a fourth order equation in 3-D." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 1029-1042. <http://eudml.org/doc/245654>.

@article{Xu2002,

abstract = {In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.},

author = {Xu, Xingwang, Yang, Paul C.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Paneitz operator; conformal invariance; Sobolev inequality; connected sum},

language = {eng},

pages = {1029-1042},

publisher = {EDP-Sciences},

title = {On a fourth order equation in 3-D},

url = {http://eudml.org/doc/245654},

volume = {8},

year = {2002},

}

TY - JOUR

AU - Xu, Xingwang

AU - Yang, Paul C.

TI - On a fourth order equation in 3-D

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 8

SP - 1029

EP - 1042

AB - In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.

LA - eng

KW - Paneitz operator; conformal invariance; Sobolev inequality; connected sum

UR - http://eudml.org/doc/245654

ER -

## References

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- [6] Z. Djadli, E. Hebey and M. Ledoux, Paneitz operators and applications. Duke Math. J. 104 (2000) 129-169. Zbl0998.58009MR1769728
- [7] C. Fefferman and R. Graham, Conformal Invariants, in Élie Cartan et les Mathématiques d’aujourd’hui. Asterisque (1985) 95-116. Zbl0602.53007
- [8] E. Hebey and F. Robert, Coercivity and Struwe’s compactness for Paneitz type operators with constant coefficients. Preprint. Zbl0998.58007
- [9] S. Paneitz, A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds. Preprint (1983). Zbl1145.53053
- [10] X. Xu and P. Yang, Positivity of Paneitz operators. Discrete Continuous Dynam. Syst. 7 (2001) 329-342. Zbl1032.58018MR1808405

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