S1-Valued Harmonic Maps with High Topological Degree: Asymptotic Behavior of the Singular Set

Potential Analysis

Volumn 13, Issue 2, 2000, Pages 169-184

  Sandier, E ^a   Soret, M ^a  

^a UNIVERSITÉ DE TOURS   (France)

Author keywords

Ginzburg Landau functionals; Harmonic maps; Renormalized energies; Singularities

Indexed keywords

EID: 0034377392     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008732819115     Document Type: Article

References (13)

1. André, N. and Shafrir, I.: 'Asymptotic behavior of minimizers for the Ginzburg-Landau functional with weight I and II'. Arch. Rat. Mech. Anal. 142 45-73, 75-98, 1998.
2. Bethuel, F., Brezis, H. and Helein, F.: 'Ginzburg-Landau vortices', Birkhauser, 1994.
3. Hardt, R. and Lin, P.H.: 'Singularities for p-energy minimizing unit vector fields on planar domains'. Calc. Var. Partial. Differ. Equ. 3, 311-341, 1995.
4. Keller, J.B., Rubinstein, J. and Sternberg, P.: 'Fast reactions Slow Diffusions and Curve Shortening', S.I.A.M. Journ. of Applied Math. 49, 116-133, 1998.
5. Lefter, C. and Radulescu, V.: 'Minimization Problems and corresponding Energy Renormalizations'. Diff. Int. Eq. 9, 903-917, 1996.
6. Tsuji, M.: 'Potential Theory in Modern Function Theory', Maruzen, Tokyo, 1959.
7. Wermer, J.: 'Potential Theory', Lect. Notes 408, Springer Verlag, New York, 1982.
8. Dal Maso, G.: 'An introduction to F-convergence, Birkhauser, Basel, 1993.
9. La Vallée Poussin, Ch. de: 'Le potentiel logarithmique', Gauthier-Villars, Louvain, 1949.
10. Doob, J.L.: 'Classical potential theory and its probabilistic counterpart'. Grundlehren der Matrhematischen Wissenchaft 262, New York, 1984.
11. Randsford, T.: 'Potential theory in the complex plane', London Mathematical Society Student texts, 28., Cambridge Univ. Press, 1995.
12. Serfaty, S.: 'Local minimizers for the Ginzburg-Landau energy near critical magnetic field', Preprint, Univ. de Paris Sud (Orsay), 1997.
13. Brezis, H.: 'Lecture notes on Ginzburg-Landau vortices', Scuola Normale Superiore de Pisa, 1998. (to appear).