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Compactness properties for geometric fourth order elliptic equations with application to the Q-curvature flow.
- Source :
- Journal für die Reine und Angewandte Mathematik; Jan2018, Vol. 2017 Issue 734, p229-264, 36p
- Publication Year :
- 2018
-
Abstract
- We prove the compactness of solutions of general fourth order elliptic equations which are L<superscript>1</superscript>-perturbations of the Q-curvature equation on compact Riemannian 4-manifolds. Consequently, we prove the global existence and convergence of the Q-curvature flow on a generic class of Riemannian 4-manifolds. As a by-product, we give a positive answer to an open question by A. Malchiodi [12] on the existence of bounded Palais-Smale sequences for the Q-curvature problem when the Paneitz operator is positive with trivial kernel. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2017
- Issue :
- 734
- Database :
- Complementary Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 127788769
- Full Text :
- https://doi.org/10.1515/ crelle-2015-0012