Degenerate elliptic systems and applications to Ginzburg-Landau type equations, part I

Calculus of Variations and Partial Differential Equations

Volumn 4, Issue 2, 1996, Pages 171-202

  Han, Zheng Chao ^a   Li, YanYan ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001099207     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01189953     Document Type: Article

References (28)

1. H. Brezis, J.-M. Coron, E.H. Lieb: Harmonic maps with defects. Comm. Math. Phys. 107 (1986) 649-705
2. F. Bethuel, H. Brezis, F. Hélein: Ginzburg-Landau vortices. Birkḧauser, Boston, 1994
3. F. Bethuel, H. Brezis, F. Hélein: Asymptotics for the minimization of a Ginzburg:Landau functional. Calc. Var. 1 (1993) 123-148
4. 2. C.R. Acad. Sc. Paris 317 (1993) 57-60, and Arch. Rat. Mech. Anal. 126 (1994) 35-58
5. 2. C.R. Acad. Sc. Paris 317 (1993) 57-60, and Arch. Rat. Mech. Anal. 126 (1994) 35-58
6. H. Brezis, L. Nirenberg: Degree theory and BMO; Part I: Compact manifolds without boundary. Selecta Mathematica (to appear)
7. Y. Chen: Weak solutions to the evolution problems of harmonic maps. Math. Z. 201 (1989) 69-74
8. 1,α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 7 (1983) 356-373
9. E. DiBenedetto: Degenerate parabolic equations. Springer, New York, 1993
10. 1+α regularity for solutions of certain degenerate P.D.E. J. Differ. Eqn. 45 (1982) 356-373
11. M. Giaquinta: Multiple integrals in the calculus of variations and nonlinear elliptic systems. Ann. Math. Studies 105, Princeton University Press, Princeton, N.J. 1983
12. M. Giaquinta, E. Giusti: On the regularity of the minima of variational integrals. Acta. Math. 148 (1982) 31-46
13. D. Gilbarg, N.S. Trudinger: Elliptic partial differential equations. 2nd edition, Grundlagen der mathematischen Wissenschaften 224, Springer, Berlin Heidelberg New York 1983
14. Z.C. Han, Y.Y. Li: Degenerate elliptic and parabolic equations and applications to Ginzburg-Landau type equations, Part II (in preparation)
15. 1-valued maps in ferforated domains (preprint)
16. R. Hardt, F.H. Lin: Mappings minimizing the LP norm of the gradient. Comm. Pure Appl. Math. 15 (1987) 555-588
17. R. Hardt, F.H. Lin: Singularities for p-Energy minimizing unit vectorfields on planar domains. Calc. Var. (to appear)
18. J. Lewis: Regularity of the derivatives of solutions to certain degenerate elliptic equations. Indiana Univ. Math. 6 (1983) 853-858
19. 1,β-regularity of p-harmonic functions (preprint)
20. F.H. Lin: Solutions of Ginzburg-Landau equations and critical points of the renormalized energy (preprint)
21. J. Rubinstein, P. Sternberg, J.B. Keller: Reaction-diffusion processes and evolution to harmonic maps. SIAM. J. Appl. Math. 49 (1989) 1722-1733
22. J. Shatah: Weak solutions and development of singularities of the SU(2)σ-model. Comm. Pure Appl. Math. 41 (1988) 459-469
23. M. Struwe: On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions. Diff. Integral Eqn. 7 (1994) 1613-1624
24. M. Struwe: Erratum to: On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions. Diff. Integral Eqn. 7 (1994) 1613-1624; Diff. Integral Eqn. 8 (1995) 224
25. P. Tolksdorff: Regularity for a more general class of quasilinear elliptic equations. J. Diff. Eqn. 51 (1984) 126-150
26. K. Uhlenbeck: Regularity for a class of non-linear elliptic systems. Acta Math. 138 (1977) 219-240
27. N.N. Ural'tseva: Degenerate quasilinear elliptic system. Zap. Nauk. Sem. Leningrad. Otel. Math. Inst. Steklov 7 (1968) 184-222 (Russian)
28. L. Wang: Compactness methods for certain degenerate elliptic systems. Manus. Math. 78 (1993) 273-285