TY - JOUR T1 - Existence of conformal metrics with constant $Q$-curvature JF - Ann. of Math. 168 (2008) 813-858 Y1 - 2008 A1 - Zindine Djadli A1 - Andrea Malchiodi AB - Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author. UR - http://hdl.handle.net/1963/2308 U1 - 1708 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A fourth order uniformization theorem on some four manifolds with large total Q-curvature JF - C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. Y1 - 2005 A1 - Zindine Djadli A1 - Andrea Malchiodi AB - Given a four-dimensional manifold (M,g), we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open. PB - Elsevier UR - http://hdl.handle.net/1963/4868 U1 - 4649 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Prescribing scalar and boundary mean curvature on the three dimensional half sphere JF - J. Geom. Anal. 13 (2003) 255-289 Y1 - 2003 A1 - Zindine Djadli A1 - Andrea Malchiodi A1 - Mohameden Ould Ahmedou AB - We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half three sphere, by deforming conformally its standard metric. Using blow up analysis techniques and minimax arguments, we prove some existence and compactness results. PB - Springer UR - http://hdl.handle.net/1963/3086 U1 - 1247 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Prescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result JF - Commun. Contemp. Math., 2002, 4, 375 Y1 - 2002 A1 - Zindine Djadli A1 - Mohameden Ould Ahmedou A1 - Andrea Malchiodi PB - SISSA Library UR - http://hdl.handle.net/1963/1539 U1 - 2624 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Prescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications JF - Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 Y1 - 2002 A1 - Zindine Djadli A1 - Andrea Malchiodi A1 - Mohameden Ould Ahmedou PB - SISSA Library UR - http://hdl.handle.net/1963/1540 U1 - 2623 U2 - Mathematics U3 - Functional Analysis and Applications ER -