Existence of conformal metrics with prescribed scalar curvature on the four dimensional half sphere

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the four dimensional half sphere. Using dynamical and topological methods involving the study of the critical points at infinity of the associated variational structure, we prove some exis...

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Veröffentlicht in:Nonlinear differential equations and applications 2012-12, Vol.19 (6), p.629-662
Hauptverfasser: Ben Ayed, Mohamed, Ghoudi, Rabeh, Ould Bouh, Kamal
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the four dimensional half sphere. Using dynamical and topological methods involving the study of the critical points at infinity of the associated variational structure, we prove some existence results like Bahri-Coron theorem. Furthermore, we consider the approximate subcritical problem and we construct some solutions which blow up at two different points, one of them lay on the boundary and the other one is an interior point.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-011-0145-y