Asymptotic behavior of Palais–Smale sequences associated with fractional Yamabe-type equations

Yi Fang and María del Mar González

Vol. 278 (2015), No. 2, 369–405

DOI: 10.2140/pjm.2015.278.369

Abstract

In this paper, we analyze the asymptotic behavior of Palais–Smale sequences associated to fractional Yamabe-type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais–Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solution for the fractional Yamabe equation on Euclidean space. We also verify the noninterfering fact for multibubbles.

Keywords

fractional Yamabe problem, Palais–Smale sequences

Mathematical Subject Classification 2010

Primary: 35J70

Secondary: 58J32

Milestones

Received: 20 October 2014

Accepted: 23 March 2015

Published: 6 October 2015