%0 Journal Article %J J. Reine Angew. Math. 594 (2006) 137-174 %D 2006 %T Compactness of solutions to some geometric fourth-order equations %A Andrea Malchiodi %X 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. %B J. Reine Angew. Math. 594 (2006) 137-174 %G en_US %U http://hdl.handle.net/1963/2126 %1 2117 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-18T08:13:05Z\\nNo. of bitstreams: 1\\n0410140v2.pdf: 335757 bytes, checksum: 30341fcdac6b4d8f187b4bab1191c993 (MD5) %R 10.1515/CRELLE.2006.038