English

Prescribing a fourth order conformal invariant on the standard sphere, Part II: blow-up analysis and applications

Analysis of PDEs 2007-05-23 v2 Differential Geometry

Abstract

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. We derive from this analysis some a priori estimates in dimension 5 and 6. On the five dimensionl sphere these a priori estimates combined with the perturbation result of Part I allow us to obtain some existence results. On the six dimensional sphere we prove the existence of at least one solution when an associated index is different from zero.

Keywords

Cite

@article{arxiv.math/0104091,
  title  = {Prescribing a fourth order conformal invariant on the standard sphere, Part II: blow-up analysis and applications},
  author = {Zindine Djadli and Andrea Malchiodi and Mohameden Ould Ahmedou},
  journal= {arXiv preprint arXiv:math/0104091},
  year   = {2007}
}