Geodesic
Compactness and global estimates for the geometric Paneitz equation in high dimensions
Hebey, Emmanuel1 ; Robert, Frédéric2
1 Université de Cergy-Pontoise, Département de Mathématiques, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France
2 Laboratoire J.A.Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice cedex 2, France
Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 135-141 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S1079-6762-04-00138-6

Hebey, Emmanuel 1 ; Robert, Frédéric 2

1 Université de Cergy-Pontoise, Département de Mathématiques, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France
2 Laboratoire J.A.Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice cedex 2, France 
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Hebey, Emmanuel; Robert, Frédéric. Compactness and global estimates for the geometric Paneitz equation in high dimensions. Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 135-141. doi: 10.1090/S1079-6762-04-00138-6

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