@article{AIHPC_2008__25_2_313_0, author = {Choe, Kwangseok and Kim, Namkwon}, title = {Blow-up solutions of the self-dual Chern-Simons-Higgs vortex equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {25}, year = {2008}, pages = {313-338}, doi = {10.1016/j.anihpc.2006.11.012}, mrnumber = {2396525}, zbl = {1145.35029}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_2_313_0} }
Choe, Kwangseok; Kim, Namkwon. Blow-up solutions of the self-dual Chern-Simons-Higgs vortex equation. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) pp. 313-338. doi : 10.1016/j.anihpc.2006.11.012. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_2_313_0/
[1] Profile of blow-up solutions to mean field equations with singular data, Comm. Partial Differential Equations 29 (2004) 1241-1265. | MR 2097983 | Zbl 1062.35146
, , , ,[2] Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory, Comm. Math. Phys. 229 (2002) 3-47. | MR 1917672 | Zbl 1009.58011
, ,[3] The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math. 53 (1993) 990-1008. | MR 1232163 | Zbl 0788.35061
, ,[4] Uniform estimates and blow-up behavior for solutions of in two dimensions, Comm. Partial Differential Equations 16 (1991) 1223-1253. | MR 1132783 | Zbl 0746.35006
, ,[5] Vortex condensation in the Chern-Simons-Higgs model: an existence theorem, Comm. Math. Phys. 168 (1995) 321-336. | MR 1324400 | Zbl 0846.58063
, ,[6] The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory, Comm. Math. Phys. 215 (2000) 119-142. | MR 1800920 | Zbl 1002.58015
, ,[7] Non-topological multivortex solutions to the self-dual Chern-Simons-Higgs equation, Comm. Math. Phys. 231 (2002) 189-221. | MR 1946331 | Zbl 1018.58008
, , ,[8] Sharp estimates for solutions of multi-bubbles in compact Riemann surfaces, Comm. Pure Appl. Math. 55 (2002) 728-771. | MR 1885666 | Zbl 1040.53046
, ,[9] Concentration phenomena of two-vortex solutions in a Chern-Simons model, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) III (2004) 369-397. | Numdam | MR 2075988 | Zbl 1170.35413
, , ,[10] A nonlinear elliptic equation arising from gauge field theory and cosmology, Proc. Roy. Soc. Lond. A 446 (1994) 453-478. | MR 1297740 | Zbl 0813.35015
, , , ,[11] Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991) 615-623. | MR 1121147 | Zbl 0768.35025
, ,[12] Qualitative properties of solutions to some nonlinear elliptic equations in , Duke Math. J. 71 (1993) 427-439. | MR 1233443 | Zbl 0923.35055
, ,[13] Uniqueness of the topological multivortex solution in the self-dual Chern-Simons theory, J. Math. Phys. 46 (1) (2005) 012305. | MR 2113759 | Zbl 1076.58012
,[14] Self duality equations for Ginzburg-Landau and Seiberg-Witten type functionals with 6th order potentials, Comm. Math. Phys. 217 (2001) 383-407. | MR 1821229 | Zbl 0994.58009
, , , , ,[15] An analysis of the two-vortex case in the Chern-Simons-Higgs model, Calc. Var. Partial Differential Equations 7 (1998) 87-97. | MR 1624438 | Zbl 0928.58021
, , , ,[16] Asymptotics for the vortex condensate solutions in Chern-Simons-Higgs theory, Asymptotic Anal. 28 (2001) 31-48. | MR 1865569 | Zbl 0997.35008
,[17] Asymptotic limit for condensate solutions in the Abelian Chern-Simons-Higgs model, Proc. Amer. Math. Soc. 131 (2003) 1839-1845. | MR 1955272 | Zbl 1036.35034
,[18] Asymptotic limit for condensate solutions in the Abelian Chern-Simons-Higgs model II, Proc. Amer. Math. Soc. 131 (2003) 3827-3832. | MR 1999930 | Zbl 1037.35022
,[19] Multivortex solutions of the Abelian Chern-Simons-Higgs theory, Phys. Rev. Lett. 64 (1990) 2230-2233. | MR 1050529 | Zbl 1014.58500
, , ,[20] Self-dual Chern-Simons vortices, Phys. Rev. Lett. 64 (1990) 2234-2237. | MR 1050530 | Zbl 1050.81595
, ,[21] Harnack type inequality: the method of moving planes, Comm. Math. Phys. 200 (1999) 421-444. | MR 1673972 | Zbl 0928.35057
,[22] Blow-up analysis for solutions of in dimension two, Indiana Univ. Math. J. 43 (1994) 1255-1270. | MR 1322618 | Zbl 0842.35011
, ,[23] On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 44 (1991) 819-851. | MR 1115095 | Zbl 0754.35042
, ,[24] On a sharp type inequality on two dimensional compact manifolds, Arch. Rational Mech. Anal. 145 (1998) 161-195. | MR 1664542 | Zbl 0980.46022
, ,[25] Double vortex condensates in the Chern-Simons-Higgs theory, Calc. Var. Partial Differential Equations 9 (1999) 31-94. | MR 1710938 | Zbl 0951.58030
, ,[26] On a class of elliptic problems in : symmetry and uniqueness results, Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 967-985. | MR 1855007 | Zbl 1009.35018
, ,[27] The existence of non-topological solitons in the self-dual Chern-Simons theory, Comm. Math. Phys. 149 (1992) 361-376. | MR 1186034 | Zbl 0760.53063
, ,[28] Multiple condensate solutions for the Chern-Simons-Higgs theory, J. Math. Phys. 37 (1996) 3769-3796. | MR 1400816 | Zbl 0863.58081
,[29] The existence of Chern-Simons vortices, Comm. Math. Phys. 137 (1991) 587-597. | MR 1105432 | Zbl 0733.58009
,[30] Abrikosov's vortices in the critical coupling, SIAM J. Math. Anal. 23 (1992) 1125-1140. | MR 1177781 | Zbl 0753.35111
, ,[31] Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (4) (1998) 459-492. | Numdam | MR 1632937 | Zbl 0910.35049
, ,[32] Solitons in Field Theory and Nonlinear Analysis, Springer-Verlag, New York, 2001. | MR 1838682 | Zbl 0982.35003
,