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Nonlinear elliptic equations involving critical Sobolev exponent on compact Riemannian manifolds in presence of symmetries.

Zindine Djadli — 1999

Revista Matemática Complutense

In this paper, we study a nonlinear elliptic equation with critical exponent, invariant under the action of a subgroup G of the isometry group of a compact Riemannian manifold. We obtain some existence results of positive solutions of this equation, and under some assumptions on G, we show that we can solve this equation for supercritical exponents.

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

Zindine DjadliAndrea MalchiodiMohameden Ould Ahmedou — 2002

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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...

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