The asymptotic behavior of Palais–Smale sequences on manifolds with boundary

Sérgio Almaraz

Vol. 269 (2014), No. 1, 1–17

DOI: 10.2140/pjm.2014.269.1

Abstract

We describe the asymptotic behavior of Palais–Smale sequences associated to certain Yamabe-type equations on manifolds with boundary. We prove that each of those sequences converges to a solution of the limit equation plus a finite number of “bubbles” which are obtained by rescaling fundamental solutions of the corresponding Euclidean equations.

Keywords

Riemannian manifold, Palais–Smale sequence, manifold with boundary, blow-up

Mathematical Subject Classification 2010

Primary: 35J65

Secondary: 53C21

Milestones

Received: 9 November 2012

Revised: 2 August 2013

Accepted: 7 November 2013

Published: 15 July 2014