| Issue |
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
|
|
|---|---|---|
| Page(s) | 1029 - 1042 | |
| DOI | https://doi.org/10.1051/cocv:2002023 | |
| Published online | 15 August 2002 | |
On a Fourth Order Equation in 3-D
1
Department of Mathematics, National
University of Singapore, 2 Science Drive 2, 119260 ; matxuxw@nus.edu.sg.
2
Department of Mathematics, Princeton University, Princeton, NJ 08544-1000 U.S.A.; yang@math.princeton.edu.
Received:
14
January
2002
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.
Mathematics Subject Classification: 53C21 / 35G20
Key words: Paneitz operator / conformal invariance / Sobolev inequality / connected sum.
© EDP Sciences, SMAI, 2002
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