TY - JOUR T1 - Compactness of solutions to some geometric fourth-order equations JF - J. Reine Angew. Math. 594 (2006) 137-174 Y1 - 2006 A1 - Andrea Malchiodi AB - 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. UR - http://hdl.handle.net/1963/2126 U1 - 2117 U2 - Mathematics U3 - Functional Analysis and Applications ER -