%0 Journal Article %J Ann. of Math. 168 (2008) 813-858 %D 2008 %T Existence of conformal metrics with constant $Q$-curvature %A Zindine Djadli %A Andrea Malchiodi %X 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. %B Ann. of Math. 168 (2008) 813-858 %G en_US %U http://hdl.handle.net/1963/2308 %1 1708 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:05:55Z\\nNo. of bitstreams: 1\\nDjadliMalchiodiFinal.pdf: 342979 bytes, checksum: fc2b0b8e4e01a5327ed8e01dc1bae6c5 (MD5) %0 Journal Article %J C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. %D 2005 %T A fourth order uniformization theorem on some four manifolds with large total Q-curvature %A Zindine Djadli %A Andrea Malchiodi %X 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. %B C. R. Acad. Sci. Paris, Ser. I 340 (2005) 341-346. %I Elsevier %G en %U http://hdl.handle.net/1963/4868 %1 4649 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2011-10-20T14:43:43Z\\nNo. of bitstreams: 1\\nexistencep81.pdf: 151457 bytes, checksum: 024bd42cba2f35fe4c206a1ef0f9a125 (MD5) %R 10.1016/j.crma.2005.01.013 %0 Journal Article %J J. Geom. Anal. 13 (2003) 255-289 %D 2003 %T Prescribing scalar and boundary mean curvature on the three dimensional half sphere %A Zindine Djadli %A Andrea Malchiodi %A Mohameden Ould Ahmedou %X 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. %B J. Geom. Anal. 13 (2003) 255-289 %I Springer %G en_US %U http://hdl.handle.net/1963/3086 %1 1247 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-13T14:32:25Z\\nNo. of bitstreams: 1\\n0211227v1.pdf: 359886 bytes, checksum: e4e0c1b0979d1cb348e41f2351b74254 (MD5) %R 10.1007/BF02930697 %0 Journal Article %J Commun. Contemp. Math., 2002, 4, 375 %D 2002 %T Prescribing a fourth oder conformal invariant on the standard sphere - Part I: a perturbation result %A Zindine Djadli %A Mohameden Ould Ahmedou %A Andrea Malchiodi %B Commun. Contemp. Math., 2002, 4, 375 %I SISSA Library %G en %U http://hdl.handle.net/1963/1539 %1 2624 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:50Z (GMT). No. of bitstreams: 1\\nmath.AP0101101.pdf: 273679 bytes, checksum: 772598ac956e1f555f866f6330ec1fd6 (MD5)\\n Previous issue date: 2000 %R 10.1142/S0219199702000695 %0 Journal Article %J Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 %D 2002 %T Prescribing a fourth oder conformal invariant on the standard sphere - Part II: blow up analysis and applications %A Zindine Djadli %A Andrea Malchiodi %A Mohameden Ould Ahmedou %B Ann. Sc. Norm. Super. Pisa Cl. Sci., 2002, 1, 387 %I SISSA Library %G en %U http://hdl.handle.net/1963/1540 %1 2623 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:03:51Z (GMT). No. of bitstreams: 1\\nmath.AP0104091.pdf: 438502 bytes, checksum: 97c6b7ab20d77a3a40904db3f08928d1 (MD5)\\n Previous issue date: 2000