On a fourth order equation in 3-D
ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002) , pp. 1029-1042.

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.

DOI : https://doi.org/10.1051/cocv:2002023
Classification : 53C21,  35G20
Mots clés : Paneitz operator, conformal invariance, Sobolev inequality, connected sum 
@article{COCV_2002__8__1029_0,
     author = {Xu, Xingwang and Yang, Paul C.},
     title = {On a fourth order equation in 3-D},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1029--1042},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     doi = {10.1051/cocv:2002023},
     zbl = {1071.53526},
     mrnumber = {1932985},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2002__8__1029_0/}
}
Xu, Xingwang; Yang, Paul C. On a fourth order equation in 3-D. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002) , pp. 1029-1042. doi : 10.1051/cocv:2002023. http://www.numdam.org/item/COCV_2002__8__1029_0/

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