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 : 10.1051/cocv:2002023
Classification : 53C21, 35G20
Mots-clés : Paneitz operator, conformal invariance, Sobolev inequality, connected sum 
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     title = {On a fourth order equation in {3-D}},
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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/articles/10.1051/cocv:2002023/

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