From One Bubble to Several Bubbles: The Low-Dimensional Case

Abstract

We study in this paper sequences of solutions of elliptic PDE's with critical Sobolev growth on compact Riemannian manifolds. We prove some compactness results for such sequences which apply in particular to sequences of solutions of the Yamabe equation. We also underline the effect of the dimension and the geometry of the manifold on the blow-up behaviour of such sequences.