@article{AIHPC_2005__22_2_227_0, author = {Esposito, Pierpaolo and Grossi, Massimo and Pistoia, Angela}, title = {On the existence of blowing-up solutions for a mean field equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {227--257}, publisher = {Elsevier}, volume = {22}, number = {2}, year = {2005}, doi = {10.1016/j.anihpc.2004.12.001}, mrnumber = {2124164}, zbl = {1129.35376}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2004.12.001/} }
TY - JOUR AU - Esposito, Pierpaolo AU - Grossi, Massimo AU - Pistoia, Angela TI - On the existence of blowing-up solutions for a mean field equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2005 SP - 227 EP - 257 VL - 22 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2004.12.001/ DO - 10.1016/j.anihpc.2004.12.001 LA - en ID - AIHPC_2005__22_2_227_0 ER -
%0 Journal Article %A Esposito, Pierpaolo %A Grossi, Massimo %A Pistoia, Angela %T On the existence of blowing-up solutions for a mean field equation %J Annales de l'I.H.P. Analyse non linéaire %D 2005 %P 227-257 %V 22 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2004.12.001/ %R 10.1016/j.anihpc.2004.12.001 %G en %F AIHPC_2005__22_2_227_0
Esposito, Pierpaolo; Grossi, Massimo; Pistoia, Angela. On the existence of blowing-up solutions for a mean field equation. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 2, pp. 227-257. doi : 10.1016/j.anihpc.2004.12.001. http://www.numdam.org/articles/10.1016/j.anihpc.2004.12.001/
[1] Perturbation of , the scalar curvature problem in , and related topics, J. Funct. Anal. 165 (1999) 117-149. | MR | Zbl
, , ,[2] Some Nonlinear Problems in Riemannian Geometry, Springer-Verlag, Berlin, 1998. | MR | Zbl
,[3] Critical Point at Infinity in Some Variational Problems, Pitman Research Notes Math., vol. 182, Longman House, Harlow, 1989. | MR | Zbl
,[4] Isoperimetric Inequalities and Applications, Pitman Monographs Studies Math., vol. 7, Pitman, 1980. | MR | Zbl
,[5] Construction of singular limits for a semilinear elliptic equation in dimension 2, Calc. Var. Partial Differential Equations 6 (1998) 1-38. | MR | Zbl
, ,[6] Mathematical Problems from Combustion Theory, Springer, Berlin, 1989. | MR | Zbl
, ,[7] A note on the Sobolev inequality, J. Funct. Anal. 100 (1991) 18-24. | MR | Zbl
, ,[8] Uniform estimates and blow-up behavior for solutions of in two dimensions, Comm. Partial Differential Equations 16 (1991) 1223-1253. | MR | Zbl
, ,[9] A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description, Comm. Math. Phys. 143 (1992) 501-525. | MR | Zbl
, , , ,[10] A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description. Part II, Comm. Math. Phys. 174 (1995) 229-260. | MR | Zbl
, , , ,[11] The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory, Comm. Math. Phys. 215 (2000) 119-142. | MR | Zbl
, ,[12] D. Chae, G. Tarantello, On planar electroweak vortices, Ann. Inst. H. Poincaré Analyse Non Linéaire, in press.
[13] An Introduction to the Study of Stellar Structure, Dover, New York, 1957. | MR | Zbl
,[14] Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991) 615-623. | MR | Zbl
, ,[15] Topological degree for a mean field equation on Riemann surfaces, Comm. Pure Appl. Math. 56 (2003) 1667-1727. | MR | Zbl
, ,[16] On the simmetry of blowup solutions to a mean field equation, Ann. Inst. H. Poincaré Analyse Non Linéaire 18 (2001) 271-296. | Numdam | MR | Zbl
, ,[17] M. Del Pino, M. Kowalczyk, M. Musso, Singular limits in Liouville-type equation, preprint. | MR
[18] On the uniqueness of the positive solution of a singularly perturbed problem, Rocky Mountain J. Math. 25 (1995) 957-975. | MR | Zbl
,[19] Existence results for mean field equations, Ann. Inst. H. Poincaré Analyse Non Linéaire 16 (1999) 653-666. | Numdam | MR | Zbl
, , , ,[20] K. El Mehdi, M. Grossi, Asymptotic estimates and qualitative properties of an elliptic problem in dimension two, preprint. | MR
[21] P. Esposito, Blow up solutions for a Liouville equation with singular data, preprint, 2003. | MR
[22] P. Esposito, A class of Liouville-type equations arising in Chern-Simons vortex theory: asymptotics and construction of blowing up solutions, Thesis, Roma “Tor Vergata”, 2003.
[23] Some problems in the theory of quasilinear equations, Amer. Math. Soc. Transl. 29 (1969) 295-381. | MR | Zbl
,[24] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. | MR | Zbl
, ,[25] On the effect of critical points of distance function in superlinear elliptic problems, Adv. Differential Equations 5 (2000) 1397-1420. | MR | Zbl
, ,[26] On a singularly perturbed elliptic equation, Adv. Differential Equations 2 (1997) 955-980. | MR | Zbl
,[27] Sur l’équation aud dérivées partielles , J. Math. 18 (1853) 71-72.
,[28] Convergence for a Liouville equation, Comment. Math. Helv. 76 (2001) 506-514. | MR | Zbl
, ,[29] Equations of gas combustion: S-shaped bifurcation and mushrooms, J. Differential Equations 134 (1997) 183-215. | MR | Zbl
, ,[30] Asymptotic solutions for a Dirichlet problem with an exponential nonlinearity, SIAM J. Math. Anal. 14 (1983) 719-735. | MR | Zbl
,[31] A two-dimensional Dirichlet problem with an exponential nonlinearity, SIAM J. Math. Anal. 14 (1983) 934-946. | MR | Zbl
,[32] A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1970/71) 1077-1092. | MR | Zbl
,[33] Multispike solutions for a nonlinear elliptic problem involving the critical Sobolev exponent, Indiana Univ. Math. J. 51 (2002) 541-579. | MR | Zbl
, ,[34] Mathematical Biology, Springer, Berlin, 1989.
,[35] Asymptotic analysis for a two dimensional elliptic eigenvalue problem with exponentially dominated nonlinearity, Asymptotic Anal. 3 (1990) 173-188. | MR | Zbl
, ,[36] Non-topological N-vortex condensates for the self-dual Chern-Simons theory, Comm. Pure Appl. Math. 56 (2003) 1752-1780. | MR | Zbl
,[37] The role of Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1990) 1-52. | MR | Zbl
,[38] Two dimensional Emden-Fowler equation with exponential nonlinearity, Nonlinear Diffusion Equations and their Equilibrium States 3 (1992) 493-512. | MR | Zbl
,[39] Global analysis for a two-dimensional eigenvalue problem with exponential nonlinearity, Ann. Inst. H. Poincaré Analyse Non Linéaire 9 (1992) 367-398. | Numdam | MR | Zbl
,[40] On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967) 473-483. | MR | Zbl
,[41] On the asymptotic solution of a partial differential equation with exponential nonlinearity, SIAM J. Math. Anal. 9 (1978) 1030-1053. | MR | Zbl
,Cité par Sources :