Compactness Properties for Geometric Fourth order Elliptic equations with Application to the Q-curvature Flow
Analysis of PDEs
2014-05-02 v1 Differential Geometry
Abstract
We prove the compactness of solutions to general fourth order elliptic equations which are L^1-perturbations of the Q-curvature equation on compact Riemannian 4-maniods. 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 on the existence of bounded Palais-Smale sequences for the Q-curvature problem when the Paneitz operator is positive with trivial kernel.
Keywords
Cite
@article{arxiv.1405.0024,
title = {Compactness Properties for Geometric Fourth order Elliptic equations with Application to the Q-curvature Flow},
author = {Ali Fardoun and Rachid Regbaoui},
journal= {arXiv preprint arXiv:1405.0024},
year = {2014}
}