Compactness and global estimates for the geometric Paneitz equation in high dimensions
Authors:
Emmanuel Hebey and Frédéric Robert
Journal:
Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 135141
MSC (2000):
Primary :, 58E30, 58J05
Published electronically:
December 10, 2004
MathSciNet review:
2119034
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: Given , a smooth compact Riemannian manifold of dimension , we investigate compactness for the fourth order geometric equation , where is the Paneitz operator, and is critical from the Sobolev viewpoint. We prove that the equation is compact when the Paneitz operator is of strong positive type.
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 P. Esposito and F. Robert, Mountain pass critical points for PaneitzBranson operators, Calc. Var. Partial Differential Equations 15 (2002), 493517. MR 1942129 (2005a:58054)
 7.
 E. Hebey and F. Robert, Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients, Calc. Var. Partial Differential Equations 13 (2001), 491517. MR 1867939 (2003m:58051)
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 E. Hebey, F. Robert, and Y. Wen, Compactness and global estimates for a fourth order equation of critical Sobolev growth arising from conformal geometry, Preprint of the University of Nice, 697, 2004.
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 S. Paneitz, A quartic conformally covariant differential operator for arbitrary pseudoRiemannian manifolds, Preprint, 1983.
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 R. Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Topics in Calculus of Variations (Montecatini Terme, 1987), Lecture Notes in Math. 1365, SpringerVerlag, Berlin, 1989, pp. 120154. MR 0994021 (90g:58023)
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Additional Information
Emmanuel Hebey
Affiliation:
Université de CergyPontoise, Département de Mathématiques, Site de SaintMartin, 2 avenue Adolphe Chauvin, 95302 CergyPontoise cedex, France
Email:
Emmanuel.Hebey@math.ucergy.fr
Frédéric Robert
Affiliation:
Laboratoire J.A.Dieudonné, Université de Nice SophiaAntipolis, Parc Valrose, 06108 Nice cedex 2, France
Email:
frobert@math.unice.fr
DOI:
http://dx.doi.org/10.1090/S1079676204001386
PII:
S 10796762(04)001386
Keywords:
Blowup behavior,
compactness,
Paneitz operator
Received by editor(s):
October 7, 2004
Published electronically:
December 10, 2004
Communicated by:
Tobias Colding
Article copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
