Duke Mathematical Journal

Topological degree for mean field equations on S2

Chang-Shou Lin

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Article information

Source
Duke Math. J., Volume 104, Number 3 (2000), 501-536.

Dates
First available in Project Euclid: 13 August 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1092403793

Digital Object Identifier
doi:10.1215/S0012-7094-00-10437-1

Mathematical Reviews number (MathSciNet)
MR1781481

Zentralblatt MATH identifier
0964.35038

Subjects
Primary: 58E15: Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35J60: Nonlinear elliptic equations

Citation

Lin, Chang-Shou. Topological degree for mean field equations on S 2. Duke Math. J. 104 (2000), no. 3, 501--536. doi:10.1215/S0012-7094-00-10437-1. https://projecteuclid.org/euclid.dmj/1092403793


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References

  • C. Bandle, Isoperimetric Inequalities and Applications, Monogr. Stud. Math. 7, Pitman, Boston, 1980.
  • 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, Comm. Math. Phys. 143 (1992), 501--525.
  • --. --. --. --., A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description, II, Comm. Math. Phys. 174 (1995), 229--260.
  • S.-Y. A. Chang, M. J. Gursky, and P. C. Yang, The scalar curvature equation on 2- and 3-spheres, Calc. Var. Partial Differential Equations 1 (1993), 205--229.
  • S. Chanillo and M. Kiessling, Rotational symmetry of solutions of some nonlinear problems in statistical mechanics and in geometry, Comm. Math. Phys. 160 (1994), 217--238.
  • W. X. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J. 63 (1991), 615--622.
  • C.-C. Chen and C.-S. Lin, Estimate of the conformal scalar curvature equation via the method of moving planes, II, J. Differential Geom. 49 (1998), 115--178.
  • --------, Singular limits of a nonlinear eigenvalue problem in two dimension, preprint.
  • K.-S. Cheng and C.-S. Lin, On the conformal Gaussian curvature equation in $\R^2$, J. Differential Equations 146 (1998), 226--250.
  • W. Ding, J. Jost, J. Li, and G. Wang, The differential equation $\D u=8\pi-8\pi h e^u$ on a compact Riemann surface, Asian J. Math. 1 (1997), 230--248.
  • --------, Existence results for mean field equations, preprint.
  • B. Gidas, W. M. Ni, and L. Nirenberg, ``Symmetry of positive solutions of nonlinear elliptic equations in $\R^n$'' in Mathematical Analysis and Applications, Part A, Adv. Math. Supp. Stud. 7a, Academic Press, New York, 1981, 369--402.
  • M. K.-H. Kiessling, Statistical mechanics of classical particles with logarithmic interactions, Comm. Pure Appl. Math. 46 (1993), 27--56.
  • Y. Y. Li, Harnack type inequality: The method of moving planes, Comm. Math. Phys. 200 (1999), 421--444.
  • Y. Y. Li and I. Shafrir, Blow-up analysis for solutions of $-\D u=V e^u$ in dimension two, Indiana Univ. Math. J. 43 (1994), 1255--1270.
  • C. S. Lin, Uniqueness of conformal metrics with prescribed total curvature in $\R^2$, to appear in Calc. Var. Partial Differential Equations.
  • --------, Uniqueness of solutions of the mean field equation on $S^2$, to appear in Arch. Rational Mech. Anal.
  • M. Nolasco and G. Tarantello, On a sharp Sobolev-type inequality on two-dimensional compact manifolds, Arch. Rational Mech. Anal. 145 (1998), 161--195.
  • L. M. Polvani and D. G. Dritschel, Wave and vortex dynamics on the surface of a sphere, J. Fluid Mech. 255 (1993), 35--64.
  • J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304--318.
  • M. Struwe and G. Tarantello, On multivortex solutions in Chern-Simons gauge theory, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 1 (1998), 109--121.
  • G. Tarantello, Multiple condensate solutions for the Chern-Simons-Higgs theory, J. Math. Phys. 37 (1996), 3769--3796.
  • Z. Q. Wang, Symmetries and the calculations of degree, Chinese Ann. Math. Ser B. 10 (1989), 520--536.