Asymptotic analysis for fourth order Paneitz equations with critical growth

Abstract

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.

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

References in corpus (2)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Non-linear partial differential equations in conformal geometry

Cited by in corpus (8)

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• The Lin-Ni's problem for mean convex domains
• Lectures on the fourth order Q curvature equation
• Q curvature on a class of manifolds with dimension at least 5
• The resonant boundary $Q$-curvature problem and boundary-weighted barycenters
• The Nirenberg problem and its generalizations: A unified approach
• Non-stability of Paneitz-Branson equations in arbitrary dimensions
• Hardy-Sobolev equations with asymptotically vanishing singularity: Blow-up analysis for the minimal energy