The Liouville equation with singular data: A concentration-compactness principle via a local representation formula

Journal of Differential Equations

Volumn 185, Issue 1, 2002, Pages 161-180

  Bartolucci, D ^a   Tarantello, G ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037057993     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2001.4159     Document Type: Article

References (37)

1. J. Ambjorn and P. Olesen, On electroweak magnetis, Nucl. Phys. B 315 (1989), 606-614.
2. C. Bandle, "Isoperimetric Inequalities and Applications," p. 7, Pitman A. Publishing, London, 1980.
3. D. Bartolucci, A priori estimates for an elliptic equation with exponential nonlinearity, preprint 2001.
4. D. Bartolucci, A compactness result for periodic multivortices in the electroweak theory, preprint 2001.
5. D. Bartolucci and G. Tarantello, Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory, Comm. Math. Phys., to appear.
6. u in two dimensions, Comm. Partial Differential Equations 16 (1991), 1223-1253.
7. L. Caffarelli and Y. Yang, Vortex condensation in the Chern-Simons-Higgs model: an existence theorem, Comm. Math. Phys. 168 (1995), 321-336.
8. 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.
9. D. Chae and O. Imanuvilov, The existence of non-topological multivortex solutions in the relativistic self-dual Chern-Simons theory, Comm. Math. Phys., to appear.
10. 2, Acta Math. 159 (1987), 214-259.
11. 2, Trans. Amer. Math. Soc. 303 (1987), 365-382.
12. 2, Duke Math. J. 71 (1993), 427-439.
13. K. S. Chou and T. Y. H. Wan, Asymptotic radial symmetry for solutions of Δu + exp u = 0 in a punctured disc, Pacific J. Math. 163 (1994), 269-276.
14. W. Ding, J. Jost, J. Li, and G. Wang, Existence results for mean field equations, Ann. Inst. H. Poincarè Anal. Nonlineare 16 (1999).
15. u on a compact Reimann surface, Asian J. Math. 1 (1997), 230-248.
16. G. Dunne, "Self-dual Chern-Simons Theories," Lecture Notes in Physics, Vol. m36, Springer, Berlin, 1995.
17. J. Hong, Y. Kim, and P. Y. Pac, Multivortex solutions of the abelian Chern-Simons theory, Phys. Rev. Lett. 64 (1990), 2230-2233.
18. R. Jackiw and E. J. Weinberg, Selfdual Chern-Simons vortices, Phys. Rev. Lett. 64 (1990), 2234-2237.
19. J. Kazdan, and F. Warner, Curvature functions for compact 2-manifolds, Ann. Math. 99 (1974), 14-47.
20. M. H. K. Kiessling, Statistical mechanics of classical particles with logarithmic interaction, Comm. Pure Appl. Math. 46 (1993), 27-56.
21. C. H. Lai (Ed.), "Selected Papers on Gauge Theory of Weak and Electromagnetic Interactions," World Scientific, Singapore.
22. Y. Y. Li, Harnack type inequality: The method of moving planes, Comm. Math. Phys. 200 (1999), 421-444.
23. u in dimension two, Indiana Univ. Math. J. 43 (1994), 1255-1270.
24. 2, Duke Math. J. 104 (2000), 501-536.
25. 2 = 0, C. R. Acad. Sci. Paris 36 (1853), 71-72.
26. M. Nolasco and G. Tarantello, Double vortex condensates in the Chern-Simons-Higgs theory, Calc. Var. Partial Differential Equations 9 (1999), 31-94.
27. M. Nolasco and G. Tarantello, On a sharp Sobolev-type inequality on two-dimensional compact manifold, Arch. Rational Mech. Anal. 145 (1998), 161-195.
28. M. Nolasco and G. Tarantello, Vortex condensates for the SU(3) Chern-Simons theory, Comm. Math. Phys. 213 (2000), 599-639.
29. P. Olesen, Soliton condensation in some self-dual Chern-Simons theories, Phys. Lett. B 265 (1991), 361-365.
30. 2: symmetry and uniqueness results, Proc. Roy. Soc. Edinburg, to appear.
31. u, C.R. Acad. Sci. Paris 315 (1992), 159-164.
32. J. Spruck and Y. Yang, Topological solutions in the self-dual Chern-Simons theory: existence and approximation, Ann. Inst. H. Poincaré Anal. Nonlineare 12 (1995), 75-97.
33. J. Spruck and Y. Yang, On multivortices in the electroweak theory I: existence of periodic solutions, Comm. Math. Phys. 144 (1992), 1-16.
34. 2, Comm. Math. Phys. 144 (192), 215-234.
35. M. Struwe and G. Tarantello, On multivortex solutions in Chern-Simons gauge theory, Boll. Un. Mat. Ital. 8 (1998), 109-121.
36. T. Suzuki, Global analysis for a two dimensional elliptic eigenvalue problem with the exponential non linearity, Ann. Inst. H. Poincaré Anal. Nonlineare 7 (1992), 367-398.
37. G. Tarantello, Multiple condensate solutions for the Chern-Simons-Higgs theory, J. Math. Phys. 37 (1996), 3769-3796.