On the shape of blow-up solutions to a mean field equation

Nonlinearity

Volumn 19, Issue 3, 2006, Pages 611-631

  Bartolucci, Daniele ^a   Montefusco, Eugenio ^b  

^a ROMA TRE UNIVERSITY   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 32544447919     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/19/3/005     Document Type: Article

References (39)

1. Bandle C 1980 Isoperimetric Inequalities and Applications (Boston, MA: Pitman) p 228
2. u ≥ 0 Arch. Ration. Mech. Anal. 51 70
3. Baraket S and Pacard F 1998 Construction of singular limits for a semilinear ellptic equation in dimension 2 Calc. Var. Partial. Diff. Eqns 6 1
4. Bartolucci D, Chen C C, Lin C S and Tarantello G 2004 Profile of blow up solutions to mean field equations with singular data Commun. Partial Diff. Eqns 29 1241
5. Bartolucci D and Tarantello G 2002 Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory Commun. Math. Phys. 229 3
6. Bartolucci D and Tarantello G 2002 The Liouville equation with singular data: a concentration-compactness principle via a local representation formula J. Diff. Eqns 185 161
7. Bavaud F 1991 Equilibrium properties of the Vlasov functional: the generalized Poisson-Boltzmann-Emden equation Rev. Mod. Phys. 63 129
8. Bebernes J and Eberly D 1998 Mathematical Problems from Combustion Theory (Applied Mathematical Series) (New York: Springer)
9. Berestycki H and Nirenberg L 1991 On the method of moving planes and the sliding method Bol. Soc. Brasil. Math. (N.S.) 22 1
10. Berestycki H, Nirenberg L and Varadhan S R S 1994 The principal eigenvalue and maximum principle for second-order elliptic operators in general domains Commun. Pure Appl. Math. 47 47
11. u in two dimensions Commun. Partial Diff. Eqns 16 1223
12. Caglioti E, Lions P L, Marchioro C and Pulvirenti M 1992 A special class of stationary flows for two dimensional Euler equations: a statistical mechanics description Commun. Math. Phys. 143 501
13. Caglioti E, Lions P L, Marchioro C and Pulvirenti M 1995 A special class of stationary flows for two dimensional Euler equations: a statistical mechanics description: Part II Commun. Math. Phys. 174 229
14. Chae D and Imanuvilov O 2000 The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory Commun. Math. Phys. 215 119
15. Chang C Y A, Chen C C and Lin C S 2003 Extremal functions for a mean field equation in two dimension Lectures on Partial Differential Equations (New Studies in Advanced Mathematics) vol 2 (Somerville, MA: International Press) p 61
16. Chen C C and Lin C S 2001 On the symmetry of blowup solution to a mean field equation Ann. Inst. H. Poincaré Anal. Non Linéaire 18 271
17. Chen C C and Lin C S 2002 Sharp estimates for solutions of multi-bubbles in compact Riemann surfaces Commun. Pure Appl. Math. 55 728
18. Chen C C and Lin C S 2003 Topological degree for a mean field equation on Riemann surfaces Commun. Pure Appl. Math. 56 1667
19. Chern J L and Lin C S 2003 The symmetry of least-energy solutions for semilinear elliptic equations J. Diff. Eqns 187 240
20. Dunne G 1995 Selfdual Chern-Simons Theories (Lecture Notes in Physics vol m36) (Berlin: Springer) p 217
21. Esposito P, Grossi M and Pistoia A 2004 On the existence of blowing-up solutions for a mean field equation Ann. Inst. H. Poincaré Anal. Non Linéaire 22 227
22. Gidas B, Ni W M and Nirenberg L 1979 Symmetry and related properties via the maximum principle Commun. Math. Phys. 68 209
23. Kiessling M H K 1993 Statistical mechanics of classical particles with logaritmic interaction Commun. Pure Appl. Math. 46 27
24. Kowalczyk M, Musso M and del Pino M 2005 Singular limits in Liouville-type equations Calc. Var. Partial. Diff. Eqns 24 47
25. Li Y Y 1999 Harnack type inequality: the method of moving planes Commun. Math. Phys. 200 421
26. u in dimension two Indiana Univ. Math. J. 43 1255
27. Lin C S and Takagi I 2001 Method of rotating planes applied to a singularly perturbed Neumann problem Calc. Var. Partial Diff. Eqns 13 519
28. Lions P L 1997 On Euler Equations and Statistical Physics (Cattedra Galileiana vol 1) (Pisa: Scuola Normale Superiore) p 69
29. Ma L and Wei J C 2001 Convergences for a Liouville equation, Comm. Math. Helv. 76 506
30. Nolasco M and Tarantello G 2000 Vortex condensates for the SU(3) Chern-Simons theory Commun. Math. Phys. 213 599
31. Onsager L 1949 Statistical hydrodynamics Nuovo Cimento 6 (Suppl) 279
32. Pacella F 2002 Symmetry results for solutions of semilinear elliptic equations with convex nonlinearities J. Funct. Anal. 192 271
33. Smets D and Willem M 2003 Partial symmetry and asymptotyc behavior for some elliptic variational problems Calc. Var. Partial Diff. Eqns 18 57
34. Struwe M and Tarantello G 1998 On multivortex solutions in Chern-Simons gauge theory Boll. Unione Math. Ital. Sez. B 1 109
35. Suzuki T 1992 Global anlysis for a two dimensional elliptic eigenvalue problem with the exponential nonlinearity Ann. Inst. H. Poincaré Anal. Non Linéaire 9 367
36. Wang G and Wei J C 2002 On a conjecture of Wolansky Nonlin. Anal. TMA 48 927
37. Wolansky G 1992 On steady distributions of self-attracting clusters under friction and fluctuations Arch. Ration. Mech. Anal. 119 335
38. Wolansky G 1992 On the evolution of self-interacting clusters and applications to semilinear equations with exponential nonlinearity J. Anal. Math. 59 251
39. Yang Y 2001 Solitons in Field Theory and Nonlinear Analysis (Berlin: Springer) p 553