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Compactness properties for geometric fourth order elliptic equations with application to the Q-curvature flow

  • Ali Fardoun EMAIL logo and Rachid Regbaoui
Published/Copyright: June 9, 2015

Abstract

We prove the compactness of solutions of general fourth order elliptic equations which are L1-perturbations of the Q-curvature equation on compact Riemannian 4-manifolds. Consequently, we prove the global existence and convergence of the Q-curvature flow on a generic class of Riemannian 4-manifolds. As a by-product, we give a positive answer to an open question by A. Malchiodi [J. reine angew. Math. 594 (2006), 137–174] on the existence of bounded Palais–Smale sequences for the Q-curvature problem when the Paneitz operator is positive with trivial kernel.

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Received: 2014-4-30
Revised: 2015-1-15
Published Online: 2015-6-9
Published in Print: 2018-1-1

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