Concentration-compactness phenomena in the higher order Liouville's equation

Martinazzi, Luca. (2009) Concentration-compactness phenomena in the higher order Liouville's equation. Journal of Functional Analysis, 256 (11). pp. 3743-3771.

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Official URL: http://edoc.unibas.ch/49894/

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We investigate different concentration–compactness and blow-up phenomena related to the Q-curvature in arbitrary even dimension. We first treat the case of an open domain in {R^2}, then that of a closed manifold and, finally, the particular case of the sphere {S^2m}. In all cases we allow the sign of the Q-curvature to vary, and show that in the case of a closed manifold, contrary to the case of open domains in {R^2m}, blow-up phenomena can occur only at points of positive Q-curvature. As a consequence, on a locally conformally flat manifold of non-positive Euler characteristic we always have compactness.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik
UniBasel Contributors:Martinazzi, Luca
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:09 Jan 2018 08:53
Deposited On:09 Jan 2018 08:53

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