@article{AIHPC_2008__25_5_1015_0, author = {Clapp, M\'onica and Mu\~noz, Claudio and Musso, Monica}, title = {Singular limits for the bi-laplacian operator with exponential nonlinearity in ${R}^{4}$}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1015--1041}, publisher = {Elsevier}, volume = {25}, number = {5}, year = {2008}, doi = {10.1016/j.anihpc.2007.09.002}, mrnumber = {2457821}, zbl = {1155.35041}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2007.09.002/} }
TY - JOUR AU - Clapp, Mónica AU - Muñoz, Claudio AU - Musso, Monica TI - Singular limits for the bi-laplacian operator with exponential nonlinearity in ${R}^{4}$ JO - Annales de l'I.H.P. Analyse non linéaire PY - 2008 SP - 1015 EP - 1041 VL - 25 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2007.09.002/ DO - 10.1016/j.anihpc.2007.09.002 LA - en ID - AIHPC_2008__25_5_1015_0 ER -
%0 Journal Article %A Clapp, Mónica %A Muñoz, Claudio %A Musso, Monica %T Singular limits for the bi-laplacian operator with exponential nonlinearity in ${R}^{4}$ %J Annales de l'I.H.P. Analyse non linéaire %D 2008 %P 1015-1041 %V 25 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2007.09.002/ %R 10.1016/j.anihpc.2007.09.002 %G en %F AIHPC_2008__25_5_1015_0
Clapp, Mónica; Muñoz, Claudio; Musso, Monica. Singular limits for the bi-laplacian operator with exponential nonlinearity in ${R}^{4}$. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 5, pp. 1015-1041. doi : 10.1016/j.anihpc.2007.09.002. http://www.numdam.org/articles/10.1016/j.anihpc.2007.09.002/
[1] Concentration phenomena for Liouville's equation in dimension four, J. Eur. Math. Soc. (JEMS) 8 (2) (2006) 171-180. | MR
, , ,[2] On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math. 41 (3) (1988) 253-294. | MR | Zbl
, ,[3] On a variational problem with lack of compactness: the topological effect of the critical points at infinity, Calc. Var. 3 (1) (1995) 67-93. | MR | Zbl
, , ,[4] Singular limits for 4-dimensional semilinear elliptic problems with exponential nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007) 875-895. | Numdam | MR | Zbl
, , , ,[5] Construction of singular limits for a semilinear elliptic equation in dimension 2, Calc. Var. Partial Differential Equations 6 (1) (1998) 1-38. | Zbl
, ,[6] The Liouville equation with singular data: a concentration-compactness principle via a local representation formula, J. Differential Equations 185 (1) (2002) 161-180.
, ,[7] Differential operators canonically associated to a conformal structure, Math. Scand. 57 (1985) 293-345. | Zbl
,[8] Uniform estimates and blow-up behavior for solutions of in two dimensions, Comm. Partial Differential Equations 16 (8-9) (1991) 1223-1253. | Zbl
, ,[9] S.Y.A. Chang, On a fourth order operator - the Paneitz operator - in conformal geometry, in: Proceedings of the Conference for the 70th of A.P. Calderon, in press.
[10] On a fourth order curvature invariant, in: (Ed.), Spectral Problems in Geometry and Arithmetic, Contemporary Math., vol. 237, Amer. Math. Soc., 1999, pp. 9-28. | MR | Zbl
, ,[11] Topological degree for a mean field equation on Riemann surfaces, Comm. Pure Appl. Math. 56 (12) (2003) 1667-1727. | MR | Zbl
, ,[12] Two-bubble solutions in the super-critical Bahri-Coron's problem, Calc. Var. Partial Differential Equations 16 (2) (2003) 113-145. | MR
, , ,[13] “Bubble-tower” radial solutions in the slightly supercritical Brezis-Nirenberg problem, J. Differential Equations 193 (2) (2003) 280-306. | MR | Zbl
, , ,[14] Singular limits in Liouville-type equations, Calc. Var. Partial Differential Equations 24 (2005) 47-81. | MR | Zbl
, , ,[15] Variational reduction for Ginzburg-Landau vortices, J. Funct. Anal. 239 (2) (2006) 497-541. | MR
, , ,[16] The two-dimensional Lazer-McKenna conjecture for an exponential nonlinearity, J. Differential Equations 231 (2006) 108-134. | MR | Zbl
, ,[17] Lectures on Algebraic Topology, Springer-Verlag, Berlin, 1972. | MR | Zbl
,[18] Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth, Proc. Amer. Math. Soc. 134 (3) (2006) 897-908. | MR | Zbl
, ,[19] Z. Djadli, A. Malchiodi, Existence of conformal metrics with constant Q-curvature, Ann. Math., in press.
[20] P. Esposito, A class of Liouville-type equations arising in Chern-Simons vortex theory: asymptotics and construction of blowing-up solutions, Ph.D. Thesis, Universitá di Roma “Tor Vergata”, 2004.
[21] On the existence of blowing-up solutions for a mean field equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2) (2005) 227-257. | Numdam | MR | Zbl
, , ,[22] Concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent, J. Differential Equations 227 (1) (2006) 29-68. | MR
, , ,[23] Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures, Ann. Math. 101 (1975) 317-331. | MR | Zbl
, ,[24] Blow-up analysis for solutions of in dimension two, Indiana Univ. Math. J. 43 (4) (1994) 1255-1270. | MR | Zbl
, ,[25] Sur l’equation aux difference partielles , C. R. Acad. Sci. Paris 36 (1853) 71-72.
,[26] Locating the peaks of solutions via the maximum principle. II. A local version of the method of moving planes, Comm. Pure Appl. Math. 56 (6) (2003) 784-809. | MR | Zbl
, ,[27] C.S. Lin, J. Wei, Sharp estimates for bubbling solutions of a fourth order mean field equation, Preprint, 2007. | Numdam | MR
[28] C.S. Lin, L.P. Wang, J. Wei, Topological degree for solutions of a fourth order mean field equation, Preprint, 2007.
[29] Convergence for a Liouville equation, Comment. Math. Helv. 76 (3) (2001) 506-514. | MR | Zbl
, ,[30] Q-curvature flow on , J. Differential Geom. 73 (1) (2006) 1-44. | MR | Zbl
, ,[31] Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially dominated nonlinearities, Asymptotic Anal. 3 (2) (1990) 173-188. | MR | Zbl
, ,[32] Essential unitarization of symplectics and applications to field quantization, J. Funct. Anal. 48 (1982) 310-359. | MR | Zbl
,[33] Multiplicity of solutions to the supercritical Bahri-Coron's problem in pierced domains, Adv. Differential Equations 11 (6) (2006) 647-666. | MR | Zbl
, ,[34] The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1) (1990) 1-52. | MR | Zbl
,[35] Two-dimensional Emden-Fowler equation with exponential nonlinearity, in: Nonlinear Diffusion Equations and their Equilibrium States, 3, Gregynog, 1989, Progr. Nonlinear Differential Equations Appl., vol. 7, Birkhäuser Boston, Boston, MA, 1992. | MR | Zbl
,[36] A quantization property for blow-up solutions of singular Liouville-type equations, J. Funct. Anal. 219 (2) (2005) 368-399. | MR | Zbl
,[37] Analytical aspects of Liouville-type equations with singular sources, in: Stationary Partial Differential Equations, vol. I, Handbook of Differential Equations, North-Holland, Amsterdam, 2004, pp. 491-592. | MR | Zbl
,[38] On the asymptotic solution of a partial differential equation with an exponential nonlinearity, SIAM J. Math. Anal. 9 (6) (1978) 1030-1053. | MR | Zbl
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