On the symmetry of blowup solutions to a mean field equation
Annales de l'I.H.P. Analyse non linéaire, Volume 18 (2001) no. 3, p. 271-296
@article{AIHPC_2001__18_3_271_0,
author = {Chen, Chuin Chuan and Lin, Chang-Shou},
title = {On the symmetry of blowup solutions to a mean field equation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {18},
number = {3},
year = {2001},
pages = {271-296},
zbl = {0995.35004},
mrnumber = {1831657},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2001__18_3_271_0}
}

Chen, Chuin Chuan; Lin, Chang-Shou. On the symmetry of blowup solutions to a mean field equation. Annales de l'I.H.P. Analyse non linéaire, Volume 18 (2001) no. 3, pp. 271-296. http://www.numdam.org/item/AIHPC_2001__18_3_271_0/

[1] Bandle C, Isoperimetric Inequalities and Applications, Pitman, Boston, 1980. | MR 572958 | Zbl 0436.35063

[2] Brezis H, Merle F, Uniform estimates and blow-up behavior for solutions of −Δu=V(x)eu in two dimensions, Comm. Partial Differential Equations 16 (1991) 1223-1254. | Zbl 0746.35006

[3] Brezis H, Li Y.Y, Shafrir I, A sup + inf inequality for some nonlinear elliptic equations involving exponential nonlinearities, J. Functional Anal. 115 (1993) 344-358. | MR 1234395 | Zbl 0794.35048

[4] Caffarelli L, Yang Y, Vortex condensation in the Chern-Simons Higgs model: An existence theorem, Comm. Math. Phys. 168 (1995) 321-336. | Zbl 0846.58063

[5] Chanillo S, Kiessling M, Rotational symmetry of solutions of some nonlinear problems in statistical mechanics and in geometry, Comm. Math. Phys. 160 (1994) 217-238. | MR 1262195 | Zbl 0821.35044

[6] Caglioti E, Lions P.L, Marchioro C, Pulvirenti M, A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description, Comm. Math. Phys. 143 (1992) 501-525. | MR 1145596 | Zbl 0745.76001

[7] Caglioti E, Lions P.L, Marchioro C, Pulvirenti M, 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 1362165 | Zbl 0840.76002

[8] Chen C.C, Lin C.S, A sharp sup+inf inequality for a nonlinear equation in R2, Comm. Anal. Geom. 6 (1998) 1-19. | MR 1619837 | Zbl 0903.35009

[9] Chen C.C., Lin C.S., Singular limits of a nonlinear eigenvalue problem in two dimensions, preprint.

[10] Chen W, Li C, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991) 615-623. | MR 1121147 | Zbl 0768.35025

[11] Ding W, Jost J, Li J, Wang G, The differential equation Δu=8π−8πheu on a compact Riemann surface, Asian J. Math. 1 (1997) 230-248. | MR 1491984 | Zbl 0955.58010

[12] Ding W., Jost J., Li J., Wang G., Existence results for mean field equations, preprint. | MR 1712560 | Zbl 0937.35055

[13] Gidas B, Ni W.M, Nirenberg L, Symmetry of positive solutions of nonlinear elliptic equations in Rn, in: Nachbin L (Ed.), Math. Anal. and Applications, Part A, Advances in Math. Suppl. Studies 7A, Academic Press, New York, 1981, pp. 369-402. | MR 634248 | Zbl 0469.35052

[14] Li Y.Y, Harnack type inequality: the method of moving planes, Comm. Math. Phys. 200 (1999) 421-444. | MR 1673972 | Zbl 0928.35057

[15] Li Y.Y, Shafrir I, Blowup analysis for solutions −Δu=Veu in dimension two, Indiana Univ. Math. J. 43 (1994) 1255-1270. | MR 1322618 | Zbl 0842.35011

[16] Lin C.S, The topological degree for the mean field equation on S2, Duke Math. J. 104 (2000) 501-536. | MR 1781481 | Zbl 0964.35038

[17] Moseley J.L, Asymptotic solutions for a Dirichlet problem with an exponential nonlinearity, SIAM J. Math. Anal. 14 (1983) 719-735. | MR 704487 | Zbl 0524.35046

[18] Moseley J.L, A two-dimensional Dirichlet problem with an exponential nonlinearity, SIAM J. Math. Anal. 14 (1983) 934-946. | MR 711174 | Zbl 0543.35036

[19] Nagasaki K, Suzuki T, Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially dominated nonlinearity, Asymptotic Analysis 3 (1990) 173-188. | MR 1061665 | Zbl 0726.35011

[20] Nolasco M, Tarantello G, On a sharp type inequality on two dimensional compact manifolds, Arch. Rational Mech. Anal. 145 (1998) 161-195. | MR 1664542 | Zbl 0980.46022

[21] Spruck J, Yang Y, Topological solutions in the self-dual Chern-Simons theory: existence and approximation, Ann. Inst. H. Poincáre Anal. Non Linéaire 12 (1995) 75-97. | Numdam | MR 1320569 | Zbl 0836.35007

[22] Struwe M, Tarantello G, On multivortex solutions in Chern-Simons Gauge theory, Boll. Unione Math. Ital. Sez. B Artic. Ric. Mat. 8 (1) (1998) 109-121. | MR 1619043 | Zbl 0912.58046

[23] Suzuki T, Global analysis for a two-dimensional elliptic eigenvalues problem with the exponential nonlinearity, Ann. Inst. Henri Poincaŕe, Anal. Non-Linéaire 9 (1992) 367-398. | Numdam | MR 1186683 | Zbl 0785.35045

[24] Tarantello G, Multiple condensate solutions for the Chern-Simons-Higgs theory, J. Math. Phys. 37 (1996) 3769-3796. | MR 1400816 | Zbl 0863.58081

[25] Weston V.H, On the asymptotic solution of a partial differential equation with an exponential nonlinearity, SIAM J. Math. Anal. 9 (1978) 1030-1053. | MR 512508 | Zbl 0402.35038