On the symmetry of blowup solutions to a mean field equation
Chuin Chuan Chen; Chang-Shou Lin
Annales de l'I.H.P. Analyse non linéaire (2001)
- Volume: 18, Issue: 3, page 271-296
- ISSN: 0294-1449
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topChen, Chuin Chuan, and Lin, Chang-Shou. "On the symmetry of blowup solutions to a mean field equation." Annales de l'I.H.P. Analyse non linéaire 18.3 (2001): 271-296. <http://eudml.org/doc/78521>.
@article{Chen2001,
author = {Chen, Chuin Chuan, Lin, Chang-Shou},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {mean field equation; moving plane; blow-up solutions; symmetries},
language = {eng},
number = {3},
pages = {271-296},
publisher = {Elsevier},
title = {On the symmetry of blowup solutions to a mean field equation},
url = {http://eudml.org/doc/78521},
volume = {18},
year = {2001},
}
TY - JOUR
AU - Chen, Chuin Chuan
AU - Lin, Chang-Shou
TI - On the symmetry of blowup solutions to a mean field equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 3
SP - 271
EP - 296
LA - eng
KW - mean field equation; moving plane; blow-up solutions; symmetries
UR - http://eudml.org/doc/78521
ER -
References
top- [1] Bandle C, Isoperimetric Inequalities and Applications, Pitman, Boston, 1980. Zbl0436.35063MR572958
- [2] Brezis H, Merle F, Uniform estimates and blow-up behavior for solutions of −Δu=V(x)eu in two dimensions, Comm. Partial Differential Equations16 (1991) 1223-1254. Zbl0746.35006
- [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. Zbl0794.35048MR1234395
- [4] Caffarelli L, Yang Y, Vortex condensation in the Chern–Simons Higgs model: An existence theorem, Comm. Math. Phys.168 (1995) 321-336. Zbl0846.58063
- [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. Zbl0821.35044MR1262195
- [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. Zbl0745.76001MR1145596
- [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. Zbl0840.76002MR1362165
- [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. Zbl0903.35009MR1619837
- [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. Zbl0768.35025MR1121147
- [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. Zbl0955.58010
- [12] Ding W., Jost J., Li J., Wang G., Existence results for mean field equations, preprint. Zbl0937.35055
- [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. Zbl0469.35052MR634248
- [14] Li Y.Y, Harnack type inequality: the method of moving planes, Comm. Math. Phys.200 (1999) 421-444. Zbl0928.35057MR1673972
- [15] Li Y.Y, Shafrir I, Blowup analysis for solutions −Δu=Veu in dimension two, Indiana Univ. Math. J.43 (1994) 1255-1270. Zbl0842.35011
- [16] Lin C.S, The topological degree for the mean field equation on S2, Duke Math. J.104 (2000) 501-536. Zbl0964.35038MR1781481
- [17] Moseley J.L, Asymptotic solutions for a Dirichlet problem with an exponential nonlinearity, SIAM J. Math. Anal.14 (1983) 719-735. Zbl0524.35046MR704487
- [18] Moseley J.L, A two-dimensional Dirichlet problem with an exponential nonlinearity, SIAM J. Math. Anal.14 (1983) 934-946. Zbl0543.35036MR711174
- [19] Nagasaki K, Suzuki T, Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially dominated nonlinearity, Asymptotic Analysis3 (1990) 173-188. Zbl0726.35011MR1061665
- [20] Nolasco M, Tarantello G, On a sharp type inequality on two dimensional compact manifolds, Arch. Rational Mech. Anal.145 (1998) 161-195. Zbl0980.46022MR1664542
- [21] Spruck J, Yang Y, Topological solutions in the self-dual Chern–Simons theory: existence and approximation, Ann. Inst. H. Poincáre Anal. Non Linéaire12 (1995) 75-97. Zbl0836.35007
- [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. Zbl0912.58046
- [23] Suzuki T, Global analysis for a two-dimensional elliptic eigenvalues problem with the exponential nonlinearity, Ann. Inst. Henri Poincaŕe, Anal. Non-Linéaire9 (1992) 367-398. Zbl0785.35045MR1186683
- [24] Tarantello G, Multiple condensate solutions for the Chern–Simons–Higgs theory, J. Math. Phys.37 (1996) 3769-3796. Zbl0863.58081
- [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. Zbl0402.35038MR512508
Citations in EuDML Documents
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- Pierpaolo Esposito, Massimo Grossi, Angela Pistoia, On the existence of blowing-up solutions for a mean field equation
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