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arXiv · 1405.0024

Compactness Properties for Geometric Fourth order Elliptic equations with Application to the Q-curvature Flow

Ali Fardoun·Rachid Regbaoui
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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.

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Ali Fardoun, Rachid Regbaoui. 2014-04-30. Compactness Properties for Geometric Fourth order Elliptic equations with Application to the Q-curvature Flow. https://arxiv.org/abs/1405.0024

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