Blow-up solutions of the self-dual Chern-Simons-Higgs vortex equation

Choe, Kwangseok; Kim, Namkwon

doi:10.1016/j.anihpc.2006.11.012

Choe, Kwangseok ; Kim, Namkwon

Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 2, pp. 313-338.

MR Zbl | 3 citations dans Numdam

DOI : 10.1016/j.anihpc.2006.11.012

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     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},
     pages = {313--338},
     publisher = {Elsevier},
     volume = {25},
     number = {2},
     year = {2008},
     doi = {10.1016/j.anihpc.2006.11.012},
     mrnumber = {2396525},
     zbl = {1145.35029},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2006.11.012/}
}

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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) no. 2, pp. 313-338. doi : 10.1016/j.anihpc.2006.11.012. http://archive.numdam.org/articles/10.1016/j.anihpc.2006.11.012/

Bibliographie
Cité par

[1] Bartolucci D., Chen C.-C., Lin C.-S., Tarantello G., Profile of blow-up solutions to mean field equations with singular data, Comm. Partial Differential Equations 29 (2004) 1241-1265. | MR | Zbl

[2] Bartolucci D., Tarantello G., Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory, Comm. Math. Phys. 229 (2002) 3-47. | MR | Zbl

[3] Bates P., Fife P.C., The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math. 53 (1993) 990-1008. | MR | Zbl

[4] Brezis H., Merle F., Uniform estimates and blow-up behavior for solutions of $- Δ u = V e^{u}$ in two dimensions, Comm. Partial Differential Equations 16 (1991) 1223-1253. | MR | Zbl

[5] Caffarelli L.A., Yang Y., Vortex condensation in the Chern-Simons-Higgs model: an existence theorem, Comm. Math. Phys. 168 (1995) 321-336. | MR | Zbl

[6] Chae D., Imanuvilov O.Y., The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory, Comm. Math. Phys. 215 (2000) 119-142. | MR | Zbl

[7] Chan H., Fu C.-C., Lin C.-S., Non-topological multivortex solutions to the self-dual Chern-Simons-Higgs equation, Comm. Math. Phys. 231 (2002) 189-221. | MR | Zbl

[8] Chen C.-C., Lin C.-S., Sharp estimates for solutions of multi-bubbles in compact Riemann surfaces, Comm. Pure Appl. Math. 55 (2002) 728-771. | MR | Zbl

[9] Chen C.-C., Lin C.-S., Wang G., 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 | Zbl

[10] Chen X., Hastings S., Mcleod J.B., Yang Y., A nonlinear elliptic equation arising from gauge field theory and cosmology, Proc. Roy. Soc. Lond. A 446 (1994) 453-478. | MR | Zbl

[11] Chen W., Li C., Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991) 615-623. | MR | Zbl

[12] Chen W., Li C., Qualitative properties of solutions to some nonlinear elliptic equations in $R^{2}$ , Duke Math. J. 71 (1993) 427-439. | MR | Zbl

[13] Choe K., Uniqueness of the topological multivortex solution in the self-dual Chern-Simons theory, J. Math. Phys. 46 (1) (2005) 012305. | MR | Zbl

[14] Ding W., Jost J., Li J., Peng X., Wang G., Self duality equations for Ginzburg-Landau and Seiberg-Witten type functionals with 6th order potentials, Comm. Math. Phys. 217 (2001) 383-407. | MR | Zbl

[15] Ding W., Jost J., Li J., Wang G., An analysis of the two-vortex case in the Chern-Simons-Higgs model, Calc. Var. Partial Differential Equations 7 (1998) 87-97. | MR | Zbl

[16] Han J., Asymptotics for the vortex condensate solutions in Chern-Simons-Higgs theory, Asymptotic Anal. 28 (2001) 31-48. | MR | Zbl

[17] Han J., Asymptotic limit for condensate solutions in the Abelian Chern-Simons-Higgs model, Proc. Amer. Math. Soc. 131 (2003) 1839-1845. | MR | Zbl

[18] Han J., Asymptotic limit for condensate solutions in the Abelian Chern-Simons-Higgs model II, Proc. Amer. Math. Soc. 131 (2003) 3827-3832. | MR | Zbl

[19] Hong J., Kim Y., Pac P.Y., Multivortex solutions of the Abelian Chern-Simons-Higgs theory, Phys. Rev. Lett. 64 (1990) 2230-2233. | MR | Zbl

[20] Jackiw R., Weinberg E.J., Self-dual Chern-Simons vortices, Phys. Rev. Lett. 64 (1990) 2234-2237. | MR | Zbl

[21] Li Y., Harnack type inequality: the method of moving planes, Comm. Math. Phys. 200 (1999) 421-444. | MR | Zbl

[22] Li Y., Shafrir I., Blow-up analysis for solutions of $- Δ u = V e^{u}$ in dimension two, Indiana Univ. Math. J. 43 (1994) 1255-1270. | MR | Zbl

[23] Ni W., Takagi I., On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 44 (1991) 819-851. | MR | Zbl

[24] Nolasco M., Tarantello G., On a sharp type inequality on two dimensional compact manifolds, Arch. Rational Mech. Anal. 145 (1998) 161-195. | MR | Zbl

[25] Nolasco M., Tarantello G., Double vortex condensates in the Chern-Simons-Higgs theory, Calc. Var. Partial Differential Equations 9 (1999) 31-94. | MR | Zbl

[26] Prajapat J., Tarantello G., On a class of elliptic problems in $R^{2}$ : symmetry and uniqueness results, Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 967-985. | MR | Zbl

[27] Spruck J., Yang Y., The existence of non-topological solitons in the self-dual Chern-Simons theory, Comm. Math. Phys. 149 (1992) 361-376. | MR | Zbl

[28] Tarantello G., Multiple condensate solutions for the Chern-Simons-Higgs theory, J. Math. Phys. 37 (1996) 3769-3796. | MR | Zbl

[29] Wang R., The existence of Chern-Simons vortices, Comm. Math. Phys. 137 (1991) 587-597. | MR | Zbl

[30] Wang S., Yang Y., Abrikosov's vortices in the critical coupling, SIAM J. Math. Anal. 23 (1992) 1125-1140. | MR | Zbl

[31] Wei J., Winter M., Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (4) (1998) 459-492. | Numdam | MR | Zbl

[32] Yang Y., Solitons in Field Theory and Nonlinear Analysis, Springer-Verlag, New York, 2001. | MR | Zbl

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