Asymptotic analysis for fourth order Paneitz equations with critical growth

Details Asymptotic analysis for fourth order Paneitz equations with critical growth Asymptotic analysis for fourth order Paneitz equations with critical growth

2011-03-03

arxiv.org/abs/1103.0655v1

Mathematics

Analysis of PDEs

35 pages. To appear in "Advances in the Calculus of Variations"

Scientific paper

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

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