A tribute to JL Lions
Free Access
Issue
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
Page(s) 219 - 238
DOI https://doi.org/10.1051/cocv:2002026
Published online 15 August 2002
  1. G. Alberti, S. Baldo and G. Orlandi, Variational convergence for functionals of Ginzburg-Landau type. Preprint (2001). [Google Scholar]
  2. L. Almeida, S. Baldo, F. Bethuel and G. Orlandi (in preparation). [Google Scholar]
  3. L. Almeida and F. Bethuel, Topological methods for the Ginzburg-Landau equation. J. Math. Pures Appl. 11 (1998) 1-49. [Google Scholar]
  4. L. Ambrosio and H.M. Soner, A measure theoretic approach to higher codimension mean curvature flow. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997) 27-49. [MathSciNet] [Google Scholar]
  5. P. Baumann, C.-N. Chen, D. Phillips and P. Sternberg, Vortex annihilation in nonlinear heat flow for Ginzburg-Landau systems. Eur. J. Appl. Math. 6 (1995) 115-126. [Google Scholar]
  6. F. Bethuel, Variational methods for Ginzburg-Landau equations, in Calculus of Variations and Geometric evolution problems, Cetraro 1996, edited by S. Hildebrandt and M. Struwe. Springer (1999). [Google Scholar]
  7. F. Bethuel, J. Bourgain, H. Brezis and G. Orlandi, W1,pestimates for solutions to the Ginzburg-Landau equation with boundary data in H1/2. C. R. Acad. Sci. Paris Sér. I Math. 333 (2001) 1069-1076. [Google Scholar]
  8. F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional. Calc. Var. Partial Differential Equations 1 (1993) 123-148. [CrossRef] [MathSciNet] [Google Scholar]
  9. F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices. Birkhäuser, Boston (1994). [Google Scholar]
  10. F. Bethuel, H. Brezis and G. Orlandi, Small energy solutions to the Ginzburg-Landau equation. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 763-770. [Google Scholar]
  11. F. Bethuel, H. Brezis and G. Orlandi, Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions. J. Funct. Anal. 186 (2001) 432-520. Erratum (to appear). [Google Scholar]
  12. F. Bethuel and T. Rivière, Vortices for a variational problem related to superconductivity. Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995) 243-303. [Google Scholar]
  13. J. Bourgain, H. Brezis and P. Mironescu, Lifting in Sobolev spaces. J. Anal. 80 (2000) 37-86. [Google Scholar]
  14. J. Bourgain, H. Brezis and P. Mironescu, On the structure of the Sobolev space H1/2 with values into the circle. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 119-124. [Google Scholar]
  15. H. Brezis and P. Mironescu, Sur une conjecture de E. De Giorgi relative à l'énergie de Ginzburg-Landau. C. R. Acad. Sci. Paris Sér. I Math. 319 (1994) 167-170. [Google Scholar]
  16. H. Federer, Geometric Measure Theory. Springer, Berlin (1969). [Google Scholar]
  17. Z.C. Han and I. Shafrir, Lower bounds for the energy of S1-valued maps in perforated domains. J. Anal. Math. 66 (1995) 295-305. [CrossRef] [MathSciNet] [Google Scholar]
  18. R. Hardt and F.H. Lin, Mappings minimizing the Lp-norm of the gradient. Comm. Pure Appl. Math. 40 (1987) 555-588. [Google Scholar]
  19. R. Jerrard, Lower bounds for generalized Ginzburg-Landau functionals. SIAM J. Math. Anal. 30 (1999) 721-746. [CrossRef] [MathSciNet] [Google Scholar]
  20. R. Jerrard and H.M. Soner, Dynamics of Ginzburg-Landau vortices. Arch. Rational Mech. Anal. 142 (1998) 99-125. [CrossRef] [MathSciNet] [Google Scholar]
  21. R. Jerrard and H.M. Soner, Scaling limits and regularity results for a class of Ginzburg-Landau systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999) 423-466. [CrossRef] [MathSciNet] [Google Scholar]
  22. R. Jerrard and H.M. Soner, The Jacobian and the Ginzburg-Landau energy. Calc. Var. Partial Differential Equations (to appear). [Google Scholar]
  23. F.H. Lin, Some dynamical properties of Ginzburg-Landau vortices. Comm. Pure Appl. Math. 49 (1996) 323-359. [CrossRef] [MathSciNet] [Google Scholar]
  24. F.H. Lin, Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds. Comm. Pure Appl. Math. 51 (1998) 385-441 [Google Scholar]
  25. F.H. Lin, Rectifiability of defect measures, fundamental groups and density of Sobolev mappings, in Journées ``Équations aux Dérivées Partielles", Saint-Jean-de-Monts, 1996, Exp. No. XII. École Polytechnique, Palaiseau (1996). [Google Scholar]
  26. F.H. Lin and T. Rivière, Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents. J. Eur. Math. Soc. 1 (1999) 237-311. Erratum, Ibid. [CrossRef] [MathSciNet] [Google Scholar]
  27. F.H. Lin and T. Rivière, A quantization property for static Ginzburg-Landau vortices. Comm. Pure Appl. Math. 54 (2001) 206-228. [CrossRef] [MathSciNet] [Google Scholar]
  28. F.H. Lin and T. Rivière, A quantization property for moving line vortices. Comm. Pure Appl. Math. 54 (2001) 826-850. [CrossRef] [MathSciNet] [Google Scholar]
  29. L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal. 98 (1987) 123-142. [Google Scholar]
  30. L. Modica and S. Mortola, Un esempio di Γ-convergenza. Boll. Un. Mat. Ital. B 14 (1977) 285-299. [Google Scholar]
  31. T. Rivière, Line vortices in the U(1)-Higgs model. ESAIM: COCV 1 (1996) 77-167. [CrossRef] [EDP Sciences] [Google Scholar]
  32. T. Rivière, Dense subsets of H1/2(S2,S1). Ann. Global Anal. Geom. 18 (2000) 517-528. [CrossRef] [MathSciNet] [Google Scholar]
  33. T. Rivière, Asymptotic analysis for the Ginzburg-Landau Equation. Boll. Un. Mat. Ital. B 8 (1999) 537-575. [Google Scholar]
  34. E. Sandier, Lower bounds for the energy of unit vector fields and applications. J. Funct. Anal. 152 (1997) 379-403; Erratum 171 (2000) 233. [Google Scholar]
  35. L. Simon, Lectures on Geometric Measure Theory, in Proc. of the Centre for Math. Analysis. Australian Nat. Univ., Canberra (1983). [Google Scholar]
  36. M. Struwe, On the asymptotic behavior of the Ginzburg-Landau model in 2 dimensions. J. Differential Equations 7 (1994) 1613-1624; Erratum 8 (1995) 224. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.