Asymptotic analysis for fourth order Paneitz equations with critical\n growth

Abstract

We investigate fourth order Paneitz equations of critical growth in the case\nof $n$-dimensional closed conformally flat manifolds, $n \\ge 5$. Such equations\narise from conformal geometry and are modelized on the Einstein case of the\ngeometric equation describing the effects of conformal changes of metrics on\nthe $Q$-curvature. We obtain sharp asymptotics for arbitrary bounded energy\nsequences of solutions of our equations from which we derive stability and\ncompactness properties. In doing so we establish the criticality of the\ngeometric equation with respect to the trace of its second order terms.\n