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Compactness and global estimates
for the geometric
Paneitz equation in high dimensions
Emmanuel Hebey and Frédéric Robert
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.
Copyright 2004 American Mathematical Society
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Article Info
- ERA Amer. Math. Soc. 10 (2004), pp. 135-141
- Publisher Identifier: S 1079-6762(04)00138-6
- 2000 Mathematics Subject Classification. Primary: 58E30, 58J05
- Key words and phrases. Blow-up behavior, compactness, Paneitz operator
- Received by editors October 7, 2004
- Posted on December 10, 2004
- Communicated by Tobias Colding
- Comments (When Available)
Emmanuel Hebey
Université de Cergy-Pontoise,
Département de Mathématiques, Site de
Saint-Martin, 2 avenue Adolphe Chauvin,
95302 Cergy-Pontoise cedex, France
E-mail address: Emmanuel.Hebey@math.u-cergy.fr
Frédéric Robert
Laboratoire J.A.Dieudonné, Université de
Nice Sophia-Antipolis,
Parc Valrose, 06108 Nice cedex 2, France
E-mail address: frobert@math.unice.fr
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