Ginzburg-Landau Vortices

1. Energy estimates for S-valued maps
Fabrice Bethuel, Haim Brezis, Frederic Helein

2. The lower bound for the energy of S-valued maps on Perforated domains
Fabrice Bethuel, Haim Brezis, Frederic Helein

3. Some basic estimateds for UE
Fabrice Bethuel, Haim Brezis, Frederic Helein

4. Towards locating the singularties: bad discs and good discs
Fabrice Bethuel, Haim Brezis, Frederic Helein

5. An upper bound for the energy of UE away for the singularities
Fabrice Bethuel, Haim Brezis, Frederic Helein

6. UEn Converges:U* is born!
Fabrice Bethuel, Haim Brezis, Frederic Helein

7. U* Coinclides with THE canonical harmonic map having singularites(aj)
Fabrice Bethuel, Haim Brezis, Frederic Helein

8. The configuration (aj) minimizes the renormalized energy W
Fabrice Bethuel, Haim Brezis, Frederic Helein

9. Some additional properties of UE
Fabrice Bethuel, Haim Brezis, Frederic Helein

10. Non-minimizing solutions of the Ginzburg-Landau equation
Fabrice Bethuel, Haim Brezis, Frederic Helein

11. Open problems
Fabrice Bethuel, Haim Brezis, Frederic Helein

Keywords: Mathematics, Partial Differential Equations, Mathematical Applications in the Physical Sciences