Existence results for mean field equations

Weiyue Ding; Jürgen Jost; Jiayu Li; Guofang Wang

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 5, page 653-666
  • ISSN: 0294-1449

How to cite

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Ding, Weiyue, et al. "Existence results for mean field equations." Annales de l'I.H.P. Analyse non linéaire 16.5 (1999): 653-666. <http://eudml.org/doc/78478>.

@article{Ding1999,
author = {Ding, Weiyue, Jost, Jürgen, Li, Jiayu, Wang, Guofang},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {planar domain; Onsager's vortex model; turbulent Euler flows; Moser-Trudinger inequality; compact Riemann surface},
language = {eng},
number = {5},
pages = {653-666},
publisher = {Gauthier-Villars},
title = {Existence results for mean field equations},
url = {http://eudml.org/doc/78478},
volume = {16},
year = {1999},
}

TY - JOUR
AU - Ding, Weiyue
AU - Jost, Jürgen
AU - Li, Jiayu
AU - Wang, Guofang
TI - Existence results for mean field equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 5
SP - 653
EP - 666
LA - eng
KW - planar domain; Onsager's vortex model; turbulent Euler flows; Moser-Trudinger inequality; compact Riemann surface
UR - http://eudml.org/doc/78478
ER -

References

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  1. [1] T. Aubin, Nonlinear analysis on manifolds, Springer-Verlag, 1982. Zbl0512.53044MR681859
  2. [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. Zbl0601.35040MR808623
  3. [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. Zbl0746.35006MR1132783
  4. [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. Zbl0745.76001MR1145596
  5. [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. Zbl0840.76002MR1362165
  6. [6] W.X. Chen and C. Li, Prescribing Gaussian curvature on surfaces with conical singularities, J. Geom. Anal., Vol. 1, 1991, pp. 359-372. Zbl0739.58012MR1129348
  7. [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. Zbl0955.58010MR1491984
  8. [8] J. Kazdan and F. Warner, Curvature functions for compact 2-manifolds, Ann. Math., Vol. 99, 1974 , pp. 14-47. Zbl0273.53034MR343205
  9. [9] M.K.H. Kiessling, Statistical mechanics of classical particles with logarithmic interactions, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 27-56. Zbl0811.76002MR1193342
  10. [10] Yan Yan Li, -Δu = λ(Veu/∫MVeu- W) on Riemann surfaces, preprint, 
  11. [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. Zbl0842.35011MR1322618
  12. [12] C. Marchioro and M. Pulvirenti, Mathematical theory of incompressible nonviscous fluids, Appl. Math. Sci., Vol. 96, Springer-Verlag, 1994. Zbl0789.76002MR1245492
  13. [13] J. Moser, A sharp form of an inequality of N. Trudinger, Indiana Univ. Math. J., Vol. 20, 1971, pp. 1077-1092. Zbl0213.13001
  14. [14] M. Nolasco and G. Tarantello, On a sharp Sobolev type inequality on two dimensional compact manifolds, preprint. Zbl0980.46022MR1664542
  15. [15] R.S. Palais, Critical point theory and the minimax principle, Global Analysis, Proc. Sympos. Pure Math., Vol. 15, 1968, pp. 185-212. Zbl0212.28902MR264712
  16. [16] M. Struwe, The evolution of harmonic mappings with free boundaries, Manuscr. Math., Vol. 70, 1991, pp. 373-384. Zbl0724.58022MR1092143
  17. [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. Zbl0703.53049MR1039366
  18. [18] M. Struwe and G. Tarantello, On multivortex solutions in Chern-Simons gauge theory, preprint. Zbl0912.58046MR1619043
  19. [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. Zbl0785.35045MR1186683

Citations in EuDML Documents

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  1. Daniele Bartolucci, Problemi ellittici non lineari con dati singolari e applicazioni alla teoria elettrodebole di Glashow-Salam-Weinberg
  2. Francesca Gladiali, Massimo Grossi, On the spectrum of a nonlinear planar problem
  3. Francesca de Marchis, Multiplicity of Solutions for a Mean Field Equation on Compact Surfaces
  4. Pierpaolo Esposito, Massimo Grossi, Angela Pistoia, On the existence of blowing-up solutions for a mean field equation
  5. Zindine Djadli, Opérateurs géométriques et géométrie conforme

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