Ginzburg-Landau equation with magnetic effect: Non-simply-connected domains

Journal of the Mathematical Society of Japan

Volumn 50, Issue 3, 1998, Pages 663-684

  Jimbo, Shuichi ^a   Zhai, Jian ^a,b  

^a HOKKAIDO UNIVERSITY   (Japan)

^b ZHEJIANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002826961     PISSN: 00255645     EISSN: 18811167     Source Type: Journal    
DOI: 10.2969/jmsj/05030663     Document Type: Article

References (24)

1. R. A. Adams, Sobolev Spaces, Academie Press, 1975.
2. S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623-727.
3. M. Berger and Y. Chen, Symmetric vortices for the Ginzburg-Landau equations of superconductivity and the nonlinear desingularization phenomenon, J. Funct. Anal. 82 (1989), 259-295.
4. F. Bethuel, H. Brezis and F. Helein, Ginzburg Landau Vortices, Birkhàuser (1994).
5. N. A. Bobylev, Topological index of extremals of multidimensional variational problems, Funct. Anal. Appl. 20 (1986), 89-93.
6. K. J. Brown, P. C. Dunne and R. A. Gardner, A semilinear parabolic system arising in the theory of superconductivity, J. Diff. Eqs. 40 (1981), 232-252.
7. A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta. Math. 88 (1952), 85-139.
8. S. Campanato, Generation of analytic semigroups in the Holder topology by elliptic operators of second order with Neumann boundary condition, Estrato da Le Matematische 35 (1980), 61-72.
9. R. W. Carroll and A. J. Glick, On the Ginzburg-Landau equations, Arch. Rat. Mech. Anal. 16 (1968), 373-384.
10. Y. Chen, Nonsymmetric vortices for the Ginzburg-Landau equations on the bounded domain, J. Math. Phys. 30 (1989), 1942-1950.
11. Q. Du, M. Gunzberger and J. Peterson, Analysis and approximation of the Ginzburg-Landau model of superconductivity, SIAM Review 34 (1992), 54-81.
12. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, New York, 1983.
13. A. Jaffe and C. Taubes, Vortices and Monopoles, Birkhàuser 1980.
14. S. Jimbo and Y. Morita, Stability of non-constant steady state solutions to a Ginzburg-Landau equation in higher space dimensions, Nonlinear Anal. TMA. 22 (1994), 753-770.
15. S. Jimbo and Y. Morita, Ginzburg-Landau equation and stable solutions in a rotational domain, SIAM J. Math. Anal. 27 (1996), 1360-1385.
16. S. Jimbo, Y. Morita and J. Zhai, Ginzburg-Landau equation and stable solutions in a nontrivial domain, Comm. PDE 20 (1995), 2093-2112.
17. V. S. Klimov, Nontrivial solutions of the Ginzburg-Landau equation, Theor. Math. Phys. 50 (1982), 383-389.
18. F. London, Superfluid, Vol. I, John Wiley and Sons, 1950.
19. T. Miyakawa, On nonstationary solutions of the Navier-Stokesequations in an exterior domain, Hiroshima Math. J. 12 (1982), 115-140.
20. S. Mizohata, The Theory of Partial Differential Equations, Cambridge Univ. Press, Cambridge, 1973.
21. F. Odeh, Existence and bifurcation theorems for the Ginzburg-Landau equations, J. Math. Phys. 8 (1967), 2351-2356.
22. J. Rubinstein and P. Sternberg, Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents, preprint.
23. Y. Yang, Existence, regularity and asymptotic behavior of the solution to the Ginzburg Landau equations on R\ Comm. Math. Phys. 123 (1989), 147-161.
24. Y. Yang, Boundary value problems of the Ginzburg-Landau equations, Proc. Roy. Soc. Edingburgh, 114A (1990), 355-365