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, Serie 5, Volume 1 (2002) no. 2, p. 387-434

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 $\left({𝕊}^{n},h\right)$. 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
@article{ASNSP_2002_5_1_2_387_0,
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},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {2},
year = {2002},
pages = {387-434},
zbl = {1150.53012},
mrnumber = {1991145},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2002_5_1_2_387_0}
}

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, Serie 5, Volume 1 (2002) no. 2, pp. 387-434. http://www.numdam.org/item/ASNSP_2002_5_1_2_387_0/

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