Remote Access Electronic Research Announcements

Electronic Research Announcements

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Electronic Research Announcements of the American Mathematical Society with MSC (2000): :, 58E30, 58J05

Retrieve articles in all journals with MSC (2000): :, 58E30, 58J05

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

Frédéric Robert
Affiliation: Laboratoire J.A.Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice cedex 2, France

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.