Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 61, pp. 1-15

Title: Quantitative uniqueness and vortex degree estimates
       for solutions of the Ginzburg-Landau equation

Author: Igor Kukavica (Univ. of Southern California, Los Angeles, CA, USA) 
         
Abstract: 
 In this paper, we provide a sharp upper bound for the 
 maximal order of vanishing for non-minimizing solutions 
 of the Ginzburg-Landau equation
 $$
   \Delta u=-{1\over\epsilon^2}(1-|u|^2)u
 $$
 which improves our previous result \cite{Ku2}. An
 application of this result is a sharp upper bound for the
 degree of any vortex.  
 We treat Dirichlet  (homogeneous and non-homogeneous) 
 as well as Neumann boundary conditions.
  
Submitted June 23, 2000. Published October 2, 2000.
Math Subject Classifications: 35B05, 35J25, 35J60, 35J65, 35Q35.
Key Words: Unique continuation; vortices; Ginzburg-Landau equation.