Prescribing a fourth order conformal invariant on the standard sphere, Part II: blow-up analysis and applications
By Z. Djadli, A. Malchiodi, M. Ahmedou. 2001
56 citations recorded by the source corpus.
In this paper we perform a fine blow up analysis for a fourth order elliptic equation involving critical Sobolev exponent, related to the prescription of some conformal invariant on the standard sphere ( S n , h ). We derive from this analysis some a priori estimates in dimension 5 and 6. On S 5 these a priori estimates, combined with the perturbation result in the first part of the present work, allow us to obtain some existence result using a continuity method. On S 6 we prove the existence of at least one solution when an index formula associated to this conformal invariant is different from zero.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/98c75217c097bf49faeb562e53f6d4b46500d7c2
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- On positive solutions to semilinear conformally invariant equations on locally conformally flat manifolds (2005, methodology): “ature in a given conformal class of metrics, that is, to solve the Paneitz-Branson equation (1.7) P4[g]u= u n+4 n−4 for some positive smooth function uon a given manifold (Mn,g) (n≥ 5) [P] [Br] [DHL] [DMA]. In our previous paper [QR], we considered the Paneitz-Branson equation (1.7) and were able to”