Geodesic
Prescribing a fourth order conformal invariant on the standard sphere, part II : blow up analysis and applications
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, pp. 387-434

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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.

Classification : 53C21, 35B45, 35J60, 53A30, 58G30 
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     author = {Djadli, Zindine and Malchiodi, Andrea and Ould Ahmedou, Mohameden},
     title = {Prescribing a fourth order conformal invariant on the standard sphere, part {II} : blow up analysis and applications},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {387--434},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {2},
     year = {2002},
     mrnumber = {1991145},
     zbl = {1150.53012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_387_0/}
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Djadli, Zindine; Malchiodi, Andrea; Ould Ahmedou, Mohameden. Prescribing a fourth order conformal invariant on the standard sphere, part II : blow up analysis and applications. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, pp. 387-434. http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_387_0/