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arXiv:math/0410140 [math.AP]AbstractReferencesReviewsResources

Compactness of solutions to some geometric fourth-order equations

Andrea Malchiodi

Published 2004-10-06, updated 2005-01-20Version 2

We prove compactness of solutions to some fourth order equations with exponential nonlinearities on four manifolds. The proof is based on a refined bubbling analysis, for which the main estimates are given in integral form. Our result is used in a subsequent paper to find critical points (via minimax arguments) of some geometric functional, which give rise to conformal metrics of constant $Q$-curvature. As a byproduct of our method, we also obtain compactness of such metrics.

Comments: 32 pages, fixed some bug in the previous version
Categories: math.AP
Subjects: 35B33, 35J35, 53A30, 53C21
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