Solutions of Ginzburg-Landau equations and critical points of the renormalized energy

 Access to full text

 Full (PDF)

1. [BBH] F. Bethuel, H. Brezis and F. Helein, Ginzburg-Landau vertices, Birkhaüser, Boston, 1994. Zbl0802.35142MR1269538
2. [BBH2] F. Bethuel, H. Brezis and F. Helein, Asymptotics for the minimization of a Ginzburg-Landau functional, Cal. variations and P.D.E., Vol. 1#2, 1993, pp. 123-148. Zbl0834.35014MR1261720
3. [BMR] H. Brezis, F. Merle and T. Riviere, Quantization effects, for -Δu = u(1-(u)2) in R2, preprint. 
4. [CL] Y.M. Chen and F.H. Lin, Evaluation of harmonic maps with the Dirichlet boundary condition, Comm. in Analysis and Geometry, Vol. 1#3, 1993, pp. 327-346. Zbl0845.35049MR1266472
5. [CS] Y.M. Chen and M. Struwe, Existence and partial regularity for heat flow for harmonic maps, Math. Z, Vol. 201, 1989, pp. 83-103. Zbl0652.58024MR990191
6. [HL] R. Hardt and F.H. Lin, Singularities for p-energy minimizing unit vector fields on planar domains, to appear in Cal. variation and P. D. E. Zbl0828.58008
7. [E] E. Weinan, Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity, preprint. Zbl0814.34039MR1297726
8. [LSU] O.A. Ladyzenskaya, N.A. Solonnikov and N.N. Uralseva, Linear and quasilinear equations of parabolic type, Translations of AMS, Mon. #23 (196X). 
9. [N] J. Neu, Vortex dynamics of complex scalar fields, Physics D., Vol. 43, 1990, pp. 384-406. Zbl0711.35024
10. [PR] L. Pismen and J. Rubinstein, Dynamics of defects, in nematics, mathematical and physical aspects, J. M. Coron et al. eds, Kluwer Pubs., 1991. MR1178081
11. [R] P. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, Conf. Board of the Math. Sci., by AMS #65. Zbl0609.58002MR845785
12. [RS] J. Rubinstein and P. Sternberg, On the Slow Motion of Vortices in the Ginzburg-Landau heat flow, preprint. Zbl0838.35102MR1356453
13. [S] L. Simon, Asymptotics for a class of non-linear evolution equations, with applications to geometric problems, Annals of Math., Vol. 118, 1983, pp. 527- 571. Zbl0549.35071MR727703
14. [St] M. Struwe, On the asymptotic behavior of minimizers of the Ginsburg-Landau model in 2 dimensions, J. Diff. Int. Eqs., Vol. 7, 1994. Zbl0809.35031MR1269674
15. [St2] M. Struwe, On the evolution of harmonic maps of Riemannian surfaces, Comment. Math. Helv., Vol. 60, 1985, pp. 558-581. Zbl0595.58013MR826871

1. Feng Zhou, Qing Zhou, A remark on multiplicity of solutions for the Ginzburg-Landau equation
2. Tristan Rivière, Line vortices in the U(1) Higgs model
3. Robert L. Jerrard, Halil Mete Soner, Scaling limits and regularity results for a class of Ginzburg-Landau systems
4. Noel J. Walkington, Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations
5. Luigi Ambrosio, Halil Mete Soner, A measure theoretic approach to higher codimension mean curvature flows
6. Noel J. Walkington, Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations