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ISSN 1079-6762

 

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), 135-141
MSC (2000): Primary :, 58E30, 58J05
Published electronically: December 10, 2004
MathSciNet review: 2119034
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Abstract: Given $(M,g)$, a smooth compact Riemannian manifold of dimension $n \ge 5$, we investigate compactness for the fourth order geometric equation $P_gu = u^{2^\sharp-1}$, where $P_g$ is the Paneitz operator, and $2^\sharp = 2n/(n-4)$ 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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Additional Information

Emmanuel Hebey
Affiliation: Université de Cergy-Pontoise, Département de Mathématiques, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France
Email: Emmanuel.Hebey@math.u-cergy.fr

Frédéric Robert
Affiliation: Laboratoire J.A.Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice cedex 2, France
Email: frobert@math.unice.fr

DOI: http://dx.doi.org/10.1090/S1079-6762-04-00138-6
PII: S 1079-6762(04)00138-6
Keywords: Blow-up 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.