Existence results for mean field equations
Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 5, p. 653-666
@article{AIHPC_1999__16_5_653_0,
     author = {Ding, Weiyue and Jost, J\"urgen and Li, Jiayu and Wang, Guofang},
     title = {Existence results for mean field equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {5},
     year = {1999},
     pages = {653-666},
     zbl = {0937.35055},
     mrnumber = {1712560},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1999__16_5_653_0}
}
Ding, Weiyue; Jost, Jürgen; Li, Jiayu; Wang, Guofang. Existence results for mean field equations. Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 5, pp. 653-666. http://www.numdam.org/item/AIHPC_1999__16_5_653_0/

[1] T. Aubin, Nonlinear analysis on manifolds, Springer-Verlag, 1982. | MR 681859 | Zbl 0512.53044

[2] A. Bahri and J.M. Coron, Sur une equation elliptique non lineaire avec l'exposant critique de Sobolev, C. R. Acad. Sci. Paris Ser. I, Vol. 301, 1985, pp. 345-348. | MR 808623 | Zbl 0601.35040

[3] H. Brezis and F. Merle, Uniform estimates and blow up behavior for solutions of -Δu = V(x)eu in two dimensions, Comm. Partial Diff. Equat., Vol. 16, 1991, pp. 1223-1253. | MR 1132783 | Zbl 0746.35006

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

[5] E. Caglioti, P.L. Lions, C. Marchioro and M. Pulvirenti, A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description. Part II, Commun. Math. Phys., Vol. 174, 1995, pp. 229-260. | MR 1362165 | Zbl 0840.76002

[6] W.X. Chen and C. Li, Prescribing Gaussian curvature on surfaces with conical singularities, J. Geom. Anal., Vol. 1, 1991, pp. 359-372. | MR 1129348 | Zbl 0739.58012

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

[8] J. Kazdan and F. Warner, Curvature functions for compact 2-manifolds, Ann. Math., Vol. 99, 1974 , pp. 14-47. | MR 343205 | Zbl 0273.53034

[9] M.K.H. Kiessling, Statistical mechanics of classical particles with logarithmic interactions, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 27-56. | MR 1193342 | Zbl 0811.76002

[10] Yan Yan Li, -Δu = λ(Veu/∫MVeu- W) on Riemann surfaces, preprint,

[11] Yan Yan Li and I. Shafrir, Blow-up analysis for solutions of -Δu = Veu in dimension two, Indiana Univ. Math. J., Vol. 43, 1994, pp. 1255-1270. | MR 1322618 | Zbl 0842.35011

[12] C. Marchioro and M. Pulvirenti, Mathematical theory of incompressible nonviscous fluids, Appl. Math. Sci., Vol. 96, Springer-Verlag, 1994. | MR 1245492 | Zbl 0789.76002

[13] J. Moser, A sharp form of an inequality of N. Trudinger, Indiana Univ. Math. J., Vol. 20, 1971, pp. 1077-1092. | Zbl 0213.13001

[14] M. Nolasco and G. Tarantello, On a sharp Sobolev type inequality on two dimensional compact manifolds, preprint. | MR 1664542

[15] R.S. Palais, Critical point theory and the minimax principle, Global Analysis, Proc. Sympos. Pure Math., Vol. 15, 1968, pp. 185-212. | MR 264712 | Zbl 0212.28902

[16] M. Struwe, The evolution of harmonic mappings with free boundaries, Manuscr. Math., Vol. 70, 1991, pp. 373-384. | MR 1092143 | Zbl 0724.58022

[17] M. Struwe, Multiple solutions to the Dirichlet problem for the equation of prescribed mean curvature , Analysis, et cetera, P. H. RABINOWITZ and E. ZEHNDER Eds., 1990, pp. 639-666. | MR 1039366 | Zbl 0703.53049

[18] M. Struwe and G. Tarantello, On multivortex solutions in Chern-Simons gauge theory, preprint. | MR 1619043

[19] T. Suzuki, Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity, Ann. Inst. H. Poincaré, Anal. Non Lineaire, Vol. 9, 1992, pp. 367-398. | Numdam | MR 1186683 | Zbl 0785.35045